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×D3×Q16 | C2 | semidirect |
| 2. C22×Dic12 | C2 | semidirect |
| 4. C3×#467 | C2 | semidirect |
| 5. #5183 | C2 | semidirect |
| 7. #5050 | C2 | semidirect |
| 8. #4887 | C2 | semidirect |
| 9. #4873 | C2 | semidirect |
| 10. #4809 | C2 | semidirect |
| 11. #4795 | C2 | semidirect |
| 47. #467 | D3 | semidirect |
| 90. Dic12 | D4 | semidirect |
| 131. #67 | Q16 | semidirect |
| 192. C22×C3 | C2×Q16 | semidirect |
| 196. C2×D3 | C2×Q16 | semidirect |
| 206. Dic3 | C2×Q16 | semidirect |
| 247. C22 | D3×Q16 | semidirect |
| 259. C3 | D4×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×Q16 | 2 |
| C22×Dic12 | 2 |
| #5632 | 2 |
| C3×#467 | 2 |
| #5183 | 2 |
| C8×#67 | 2 |
| #5050 | 2 |
| #4887 | 2 |
| #4873 | 2 |
| #4809 | 2 |
| #4795 | 2 |
| D4×Q16 | 3 |