Finite Group DatabasebetaFinite Group DatabasebetaOrder 2400.
864 conjugacy classes of subgroups; only the 296 normal subgroups are shown.
This group has 864 conjugacy classes of subgroups — too many to draw. Only its 296 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 |
|---|---|---|
| 1. C2×C3×C52×D4 | C2 | semidirect |
| 2. C2×C52×#67 | C2 | semidirect |
| 3. C2×C52×D12 | C2 | semidirect |
| 4. C4×C52×Dic3 | C2 | semidirect |
| 13. C5×#940 | C5 | direct (N × H) |
| 16. C2×C52×D4 | D3 | semidirect |
| 23. C3×C4×C52 | D4 | semidirect |
| 24. C52×Dic3 | D4 | semidirect |
| 25. C2×C3×C5×D4 | C2×C5 | semidirect |
| 26. C2×C5×#67 | C2×C5 | semidirect |
| 27. C2×C5×D12 | C2×C5 | semidirect |
| 28. C4×C5×Dic3 | C2×C5 | semidirect |
| 54. C4×C52 | #67 | semidirect |
| 55. #940 | C52 | direct (N × H) |
| 58. C2×C5×D4 | C5×D3 | semidirect |
| 60. C3×C52 | #127 | semidirect |
| 66. C3×C4×C5 | C5×D4 | semidirect |
| 67. C5×Dic3 | C5×D4 | semidirect |
| 72. C2×C3×D4 | C2×C52 | semidirect |
| 73. C2×#67 | C2×C52 | semidirect |
| 74. C2×D12 | C2×C52 | semidirect |
| 75. C4×Dic3 | C2×C52 | semidirect |
| 88. C52 | #940 | direct (N × H) |
| 102. C4×C5 | C5×#67 | semidirect |
| 105. C2×D4 | C52×D3 | semidirect |
| 107. C3×C5 | C5×#127 | semidirect |
| 113. C3×C4 | C52×D4 | semidirect |
| 114. Dic3 | C52×D4 | semidirect |
| 130. C5 | C5×#940 | direct (N × H) |
| 137. C4 | C52×#67 | semidirect |
| 138. C3 | C52×#127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C52×D4 | 2 |
| C2×C52×#67 | 2 |
| C2×C52×D12 | 2 |
| C4×C52×Dic3 | 2 |
| C52×#127 | 3 |
| C5×#940 | 5 |