Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
286 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 65 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×#99 | C2 | semidirect |
| 3. C2×#834 | C2 | semidirect |
| 4. #4474 | C2 | semidirect |
| 5. #4473 | C2 | semidirect |
| 8. C2×#235 | C4 | semidirect |
| 13. #940 | C4 | semidirect |
| 17. #936 | C4 | semidirect |
| 19. #926 | C4 | semidirect |
| 26. C2×#99 | D3 | semidirect |
| 47. C2×D12 | C2×C4 | semidirect |
| 49. C2×Dic6 | C2×C4 | semidirect |
| 60. C4×Dic3 | C2×C4 | semidirect |
| 61. C4×Dic3 | C2×C4 | semidirect |
| 245. C3 | #2127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5805 | 2 |
| C2×C3×#99 | 2 |
| C2×#834 | 2 |
| #4474 | 2 |
| #4473 | 2 |
| #2127 | 3 |