Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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. #5805 | C2 | semidirect |
| 2. C2×#932 | C2 | semidirect |
| 3. C2×#904 | C2 | semidirect |
| 4. #5504 | C2 | semidirect |
| 5. C2×C3×#102 | C2 | semidirect |
| 6. #5102 | C2 | semidirect |
| 7. #4966 | C2 | semidirect |
| 8. #4787 | C2 | semidirect |
| 9. #4786 | C2 | semidirect |
| 10. #4767 | C2 | semidirect |
| 11. #4762 | C2 | semidirect |
| 29. C2×Dic12 | C22 | semidirect |
| 31. C2×D24 | C22 | semidirect |
| 32. C2×#204 | C22 | semidirect |
| 33. C2×#204 | C22 | semidirect |
| 34. #893 | C22 | semidirect |
| 37. #887 | C22 | semidirect |
| 40. Dic3⋊C8 | C22 | semidirect |
| 41. Dic3⋊C8 | C22 | semidirect |
| 42. #810 | C22 | semidirect |
| 43. #809 | C22 | semidirect |
| 54. C2×#102 | D3 | semidirect |
| 69. #235 | D4 | semidirect |
| 301. C3 | #3045 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5805 | 2 |
| C2×#932 | 2 |
| C2×#904 | 2 |
| #5504 | 2 |
| C2×C3×#102 | 2 |
| #5102 | 2 |
| #4966 | 2 |
| #4787 | 2 |
| #4786 | 2 |
| #4767 | 2 |
| #4762 | 2 |
| #3045 | 3 |