Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
482 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#915 | C2 | semidirect |
| 3. Q8×D12 | C2 | semidirect |
| 4. C3×#460 | C2 | semidirect |
| 5. #5170 | C2 | semidirect |
| 6. #5076 | C2 | semidirect |
| 7. C4×#216 | C2 | semidirect |
| 8. #4849 | C2 | semidirect |
| 9. #4838 | C2 | semidirect |
| 10. #4783 | C2 | semidirect |
| 11. #4780 | C2 | semidirect |
| 49. #460 | D3 | semidirect |
| 78. #216 | D4 | semidirect |
| 206. C3×C4 | #137 | semidirect |
| 264. C4 | #915 | semidirect |
| 267. C3 | #3278 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#915 | 2 |
| #5718 | 2 |
| Q8×D12 | 2 |
| C3×#460 | 2 |
| #5170 | 2 |
| #5076 | 2 |
| C4×#216 | 2 |
| #4849 | 2 |
| #4838 | 2 |
| #4783 | 2 |
| #4780 | 2 |
| #3278 | 3 |