Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
432 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 107 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. C22×D3×C8 | C2 | semidirect |
| 3. C2×#821 | C2 | semidirect |
| 4. #4987 | C2 | semidirect |
| 5. C2×#809 | C2 | semidirect |
| 6. C3×#340 | C2 | semidirect |
| 7. #4529 | C2 | semidirect |
| 23. #895 | C4 | semidirect |
| 33. #340 | D3 | semidirect |
| 58. C2×C3×C8 | D4 | semidirect |
| 69. C2×C3⋊C8 | D4 | semidirect |
| 161. C2×C8 | D12 | semidirect |
| 190. C2×D3 | #102 | semidirect |
| 281. C3 | #1893 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×C8 | 2 |
| C2×#895 | 2 |
| C2×#821 | 2 |
| #4987 | 2 |
| C2×#809 | 2 |
| C3×#340 | 2 |
| #4529 | 2 |
| #1893 | 3 |