Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
244 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 63 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. #5470 | C2 | semidirect |
| 5. C3×#339 | C2 | semidirect |
| 6. #4556 | C2 | semidirect |
| 7. #4531 | C2 | semidirect |
| 29. #339 | D3 | semidirect |
| 38. C2×D12 | Q8 | semidirect |
| 41. C2×Dic6 | Q8 | semidirect |
| 197. C3 | #2031 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5470 | 2 |
| #5139 | 2 |
| #5006 | 2 |
| C2×#805 | 2 |
| C3×#339 | 2 |
| #4556 | 2 |
| #4531 | 2 |
| #2031 | 3 |