Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
232 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 77 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. C3×#405 | C2 | semidirect |
| 5. #4995 | C2 | semidirect |
| 6. #4554 | C2 | semidirect |
| 7. #4552 | C2 | semidirect |
| 18. #823 | C4 | semidirect |
| 29. #405 | D3 | semidirect |
| 194. C3 | #1931 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#405 | 2 |
| C2×#823 | 2 |
| C2×#821 | 2 |
| #5001 | 2 |
| #4995 | 2 |
| #4554 | 2 |
| #4552 | 2 |
| #1931 | 3 |