Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
482 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 482 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. C22×C3×Q16 | C2 | semidirect |
| 2. #5817 | C2 | semidirect |
| 3. C2×#919 | C2 | semidirect |
| 4. #5227 | C2 | semidirect |
| 5. #5191 | C2 | semidirect |
| 6. #5188 | C2 | semidirect |
| 7. #5187 | C2 | semidirect |
| 8. #5185 | C2 | semidirect |
| 9. Dic3×Q16 | C2 | semidirect |
| 10. #5115 | C2 | semidirect |
| 11. C8×#67 | C2 | semidirect |
| 43. C22×Q16 | D3 | semidirect |
| 70. C3×Q16 | D4 | semidirect |
| 169. Q16 | #67 | semidirect |
| 193. C22×C3 | #135 | semidirect |
| 255. C22 | #919 | semidirect |
| 266. C3 | #3285 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Q16 | 2 |
| #5817 | 2 |
| C2×#919 | 2 |
| #5227 | 2 |
| #5191 | 2 |
| #5188 | 2 |
| #5187 | 2 |
| #5185 | 2 |
| Dic3×Q16 | 2 |
| #5115 | 2 |
| C8×#67 | 2 |
| #3285 | 3 |