Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
142 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 49 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. #4874 | C2 | semidirect |
| 3. C3×#367 | C2 | semidirect |
| 5. Dic3⋊C16 | C2 | semidirect |
| 7. #4490 | C2 | semidirect |
| 23. #367 | D3 | semidirect |
| 39. D24 | Q8 | semidirect |
| 122. C3 | #2226 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #4874 | 2 |
| #4872 | 2 |
| C3×#367 | 2 |
| #4509 | 2 |
| Dic3⋊C16 | 2 |
| #4491 | 2 |
| #4490 | 2 |
| #2226 | 3 |