Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
198 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 4. C2×#808 | C2 | semidirect |
| 5. C3×#343 | C2 | semidirect |
| 6. #4558 | C2 | semidirect |
| 7. #4554 | C2 | semidirect |
| 27. #343 | D3 | semidirect |
| 182. C3 | #2079 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5133 | 2 |
| #5129 | 2 |
| #4966 | 2 |
| C2×#808 | 2 |
| C3×#343 | 2 |
| #4558 | 2 |
| #4554 | 2 |
| #2079 | 3 |