Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
362 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 103 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×#389 | C2 | semidirect |
| 5. C2×#808 | C2 | semidirect |
| 6. #4529 | C2 | semidirect |
| 7. #4524 | C2 | semidirect |
| 23. #809 | C4 | semidirect |
| 29. #389 | D3 | semidirect |
| 52. C3×C4⋊C4 | C2×C4 | semidirect |
| 63. C2×C3⋊C8 | C2×C4 | semidirect |
| 112. D12 | C4⋊C4 | semidirect |
| 144. C4⋊C4 | C4×D3 | semidirect |
| 238. C3 | #1864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D12 | 2 |
| C3×#389 | 2 |
| C2×#809 | 2 |
| C2×#808 | 2 |
| #4529 | 2 |
| #4524 | 2 |
| #1864 | 3 |