Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
648 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 157 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×#940 | C2 | semidirect |
| 2. C22×#213 | C2 | semidirect |
| 3. C22×D24 | C2 | semidirect |
| 4. C2×#893 | C2 | semidirect |
| 5. C2×C3×#102 | C2 | semidirect |
| 6. C2×Dic3⋊C8 | C2 | semidirect |
| 7. C2×#809 | C2 | semidirect |
| 8. #4786 | C2 | direct (N × H) |
| 19. #940 | C22 | semidirect |
| 21. C2×#213 | C22 | semidirect |
| 26. C2×D24 | C22 | semidirect |
| 28. #893 | C22 | semidirect |
| 29. C3×#102 | C22 | semidirect |
| 30. Dic3⋊C8 | C22 | semidirect |
| 31. #809 | C22 | semidirect |
| 39. C2×#102 | D3 | semidirect |
| 60. C2×D12 | D4 | semidirect |
| 97. #102 | C2×D3 | semidirect |
| 123. C2×Dic3 | D8 | semidirect |
| 131. D12 | C2×D4 | semidirect |
| 192. Dic3 | C2×D8 | semidirect |
| 231. C2×C3 | #459 | semidirect |
| 259. C3 | C2×#459 | semidirect |
| 263. C2 | #4786 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#940 | 2 |
| C22×#213 | 2 |
| C22×D24 | 2 |
| C2×#893 | 2 |
| C2×C3×#102 | 2 |
| C2×Dic3⋊C8 | 2 |
| C2×#809 | 2 |
| #4786 | 2 |
| C2×#459 | 3 |