Finite Group DatabasebetaFinite Group DatabasebetaOrder 2400.
1056 conjugacy classes of subgroups; only the 392 normal subgroups are shown.
This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 392 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4×C52×D3 | C2 | semidirect |
| 3. C3×C52×C22⋊C4 | C2 | semidirect |
| 4. C52×#217 | C2 | semidirect |
| 5. C52×(C2×D3)⋊C4 | C2 | semidirect |
| 9. C22×C52×D3 | C4 | semidirect |
| 12. C2×C3×C4×C52 | C22 | semidirect |
| 13. C2×C52×Dic3 | C22 | semidirect |
| 15. C5×D3×C22⋊C4 | C5 | direct (N × H) |
| 20. C52×C22⋊C4 | D3 | direct (N × H) |
| 22. C22×C3×C52 | C2×C4 | semidirect |
| 27. C2×C52×D3 | C2×C4 | semidirect |
| 32. C2×C4×C5×D3 | C2×C5 | semidirect |
| 33. C3×C5×C22⋊C4 | C2×C5 | semidirect |
| 34. C5×#217 | C2×C5 | semidirect |
| 35. C5×(C2×D3)⋊C4 | C2×C5 | semidirect |
| 43. C2×C4×C52 | C2×D3 | semidirect |
| 49. C52×D3 | C22⋊C4 | direct (N × H) |
| 52. C22×C5×D3 | C4×C5 | semidirect |
| 55. C2×C3×C4×C5 | C22×C5 | semidirect |
| 56. C2×C5×Dic3 | C22×C5 | semidirect |
| 64. C22×C52 | C4×D3 | semidirect |
| 68. D3×C22⋊C4 | C52 | direct (N × H) |
| 73. C5×C22⋊C4 | C5×D3 | direct (N × H) |
| 74. C3×C52 | C2×C22⋊C4 | semidirect |
| 76. C22×C3×C5 | C2×C4×C5 | semidirect |
| 81. C2×C5×D3 | C2×C4×C5 | semidirect |
| 91. C2×C4×D3 | C2×C52 | semidirect |
| 92. C3×C22⋊C4 | C2×C52 | semidirect |
| 93. #217 | C2×C52 | semidirect |
| 94. (C2×D3)⋊C4 | C2×C52 | semidirect |
| 102. C2×C4×C5 | C2×C5×D3 | semidirect |
| 108. C5×D3 | C5×C22⋊C4 | direct (N × H) |
| 109. C52 | D3×C22⋊C4 | direct (N × H) |
| 112. C22×D3 | C4×C52 | semidirect |
| 115. C2×C3×C4 | C22×C52 | semidirect |
| 116. C2×Dic3 | C22×C52 | semidirect |
| 124. C22×C5 | C4×C5×D3 | semidirect |
| 132. C22⋊C4 | C52×D3 | direct (N × H) |
| 133. C3×C5 | C2×C5×C22⋊C4 | semidirect |
| 135. C22×C3 | C2×C4×C52 | semidirect |
| 140. C2×D3 | C2×C4×C52 | semidirect |
| 156. C2×C4 | C2×C52×D3 | semidirect |
| 161. D3 | C52×C22⋊C4 | direct (N × H) |
| 162. C5 | C5×D3×C22⋊C4 | direct (N × H) |
| 169. C22 | C4×C52×D3 | semidirect |
| 173. C3 | C2×C52×C22⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C52×D3 | 2 |
| C2×C4×C52×D3 | 2 |
| C3×C52×C22⋊C4 | 2 |
| C52×#217 | 2 |
| C52×(C2×D3)⋊C4 | 2 |
| C2×C52×C22⋊C4 | 3 |
| C5×D3×C22⋊C4 | 5 |