Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
126 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 43 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 |
|---|---|---|
| 2. #4855 | C2 | semidirect |
| 3. C3×#365 | C2 | semidirect |
| 5. #4511 | C2 | semidirect |
| 6. #4494 | C2 | semidirect |
| 23. #365 | D3 | semidirect |
| 36. Dic12 | Q8 | semidirect |
| 37. D24 | Q8 | semidirect |
| 117. C3 | #2230 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #4895 | 2 |
| #4855 | 2 |
| C3×#365 | 2 |
| #4518 | 2 |
| #4511 | 2 |
| #4494 | 2 |
| #4488 | 2 |
| #2230 | 3 |