Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
794 conjugacy classes of subgroups; only the 382 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 382 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×C3×#217 | C2 | semidirect |
| 3. C3×D4×Dic3 | C2 | semidirect |
| 4. C3×#926 | C2 | semidirect |
| 6. #5798 | C3 | direct (N × H) |
| 8. C2×C32×D4 | C4 | semidirect |
| 11. C22×C3×Dic3 | C22 | semidirect |
| 13. C3×#217 | C22 | semidirect |
| 14. C3×C4⋊Dic3 | C22 | semidirect |
| 15. C3×C4×Dic3 | C22 | semidirect |
| 22. C2×#217 | C2×C3 | semidirect |
| 23. D4×Dic3 | C2×C3 | semidirect |
| 24. #926 | C2×C3 | semidirect |
| 26. C23×C32 | C2×C4 | semidirect |
| 29. C32×D4 | C2×C4 | semidirect |
| 30. C2×C32×C4 | C2×C4 | semidirect |
| 40. C2×C3×D4 | Dic3 | semidirect |
| 41. C2×C3×D4 | C3×C4 | semidirect |
| 48. C22×Dic3 | C22×C3 | semidirect |
| 54. #217 | C22×C3 | semidirect |
| 55. C4⋊Dic3 | C22×C3 | semidirect |
| 56. C4×Dic3 | C22×C3 | semidirect |
| 75. C23×C3 | C2×Dic3 | semidirect |
| 76. C23×C3 | C2×C3×C4 | semidirect |
| 82. C3×D4 | C2×Dic3 | semidirect |
| 83. C3×D4 | C2×C3×C4 | semidirect |
| 88. C2×C3×C4 | C2×Dic3 | semidirect |
| 89. C2×C3×C4 | C2×C3×C4 | semidirect |
| 99. C2×D4 | C3×Dic3 | semidirect |
| 130. C32 | #518 | semidirect |
| 132. C23 | C2×C3×Dic3 | semidirect |
| 135. D4 | C2×C3×Dic3 | semidirect |
| 138. C2×C4 | C2×C3×Dic3 | semidirect |
| 161. C3 | #5798 | direct (N × H) |
| 162. C3 | C3×#518 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×D4 | 2 |
| C2×C3×#217 | 2 |
| C3×D4×Dic3 | 2 |
| C3×#926 | 2 |
| C3×#518 | 3 |
| #5798 | 3 |