Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
| 2. Q8×D12 | C2 | semidirect |
| 4. C3×C4×SD16 | C2 | semidirect |
| 5. #5031 | C2 | semidirect |
| 6. #5019 | C2 | semidirect |
| 7. #4867 | C2 | semidirect |
| 8. #4809 | C2 | semidirect |
| 9. #4783 | C2 | semidirect |
| 10. #4699 | C2 | semidirect |
| 11. #4688 | C2 | semidirect |
| 52. C4×SD16 | D3 | semidirect |
| 69. C3×SD16 | D4 | semidirect |
| 173. SD16 | D12 | semidirect |
| 205. C3×C4 | #137 | semidirect |
| 260. C4 | #915 | semidirect |
| 263. C3 | #3276 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#915 | 2 |
| Q8×D12 | 2 |
| #5555 | 2 |
| C3×C4×SD16 | 2 |
| #5031 | 2 |
| #5019 | 2 |
| #4867 | 2 |
| #4809 | 2 |
| #4783 | 2 |
| #4699 | 2 |
| #4688 | 2 |
| #3276 | 3 |