Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
358 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 4. #4849 | C2 | semidirect |
| 5. #4829 | C2 | semidirect |
| 8. #4716 | C2 | semidirect |
| 9. C4×Dic12 | C2 | semidirect |
| 187. C3 | #3127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5518 | 2 |
| #5516 | 2 |
| C3×#433 | 2 |
| #4849 | 2 |
| #4829 | 2 |
| #4739 | 2 |
| #4723 | 2 |
| #4716 | 2 |
| C4×Dic12 | 2 |
| #3127 | 3 |