Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
282 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 67 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. #5500 | C2 | semidirect |
| 4. C3×#343 | C2 | semidirect |
| 5. #4555 | C2 | semidirect |
| 21. #343 | D3 | semidirect |
| 30. C2×D12 | Q8 | semidirect |
| 156. C3 | #2027 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5500 | 2 |
| #5131 | 2 |
| #4988 | 2 |
| C3×#343 | 2 |
| #4555 | 2 |
| #2027 | 3 |