Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
456 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 121 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. C22×C4⋊Dic3 | C2 | semidirect |
| 3. C2×C3×C22⋊C8 | C2 | semidirect |
| 4. C2×#821 | C2 | semidirect |
| 5. #4551 | C2 | semidirect |
| 13. #930 | C4 | semidirect |
| 24. C2×C22⋊C8 | D3 | semidirect |
| 45. C2×D12 | C2×C4 | semidirect |
| 53. C4⋊Dic3 | C2×C4 | semidirect |
| 54. C4⋊Dic3 | D4 | semidirect |
| 139. C22×C3 | #102 | semidirect |
| 216. C22 | #821 | semidirect |
| 229. C3 | #1874 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#930 | 2 |
| C22×C4⋊Dic3 | 2 |
| C2×C3×C22⋊C8 | 2 |
| C2×#821 | 2 |
| #4551 | 2 |
| #1874 | 3 |