Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
160 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 3. C4×Dic12 | C2 | semidirect |
| 5. #4492 | C2 | semidirect |
| 6. #4489 | C2 | semidirect |
| 7. #4461 | C2 | semidirect |
| 16. #827 | C4 | semidirect |
| 42. Dic12 | C2×C4 | semidirect |
| 44. C3⋊C16 | C2×C4 | semidirect |
| 130. C3 | #2175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×D8 | 2 |
| C2×#827 | 2 |
| C4×Dic12 | 2 |
| #4562 | 2 |
| #4492 | 2 |
| #4489 | 2 |
| #4461 | 2 |
| #2175 | 3 |