Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 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×Dic12 | C2 | semidirect |
| 4. #5116 | C2 | semidirect |
| 5. #4849 | C2 | semidirect |
| 6. #4739 | C2 | semidirect |
| 7. #4699 | C2 | semidirect |
| 8. C4×Dic12 | C2 | semidirect |
| 63. Dic12 | D4 | direct (N × H) |
| 85. C3×D4 | Q16 | semidirect |
| 132. C22×C3 | C2×Q16 | semidirect |
| 136. C3×C4 | C2×Q16 | semidirect |
| 148. D4 | Dic12 | direct (N × H) |
| 168. C22 | C2×Dic12 | semidirect |
| 175. C4 | C2×Dic12 | semidirect |
| 178. C3 | D4×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic12 | 2 |
| D4×Dic6 | 2 |
| C3×C8×D4 | 2 |
| #5116 | 2 |
| #4849 | 2 |
| #4739 | 2 |
| #4699 | 2 |
| C4×Dic12 | 2 |
| D4×Q16 | 3 |