Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
568 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 205 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. C3×#376 | C2 | semidirect |
| 4. #4932 | C2 | semidirect |
| 5. C4×Dic3⋊C4 | C2 | semidirect |
| 8. #4651 | C2 | semidirect |
| 9. #4650 | C2 | semidirect |
| 22. C42×D3 | C4 | semidirect |
| 37. #376 | D3 | semidirect |
| 191. C3 | #2283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×D3 | 2 |
| C3×#376 | 2 |
| C4×(C2×D3)⋊C4 | 2 |
| #4932 | 2 |
| C4×Dic3⋊C4 | 2 |
| #4667 | 2 |
| #4664 | 2 |
| #4651 | 2 |
| #4650 | 2 |
| #2283 | 3 |