Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
284 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 284 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. #5101 | C2 | semidirect |
| 5. #4556 | C2 | semidirect |
| 10. C2×C3×M16 | C4 | semidirect |
| 12. C22×C3×C8 | C4 | semidirect |
| 16. #836 | C4 | semidirect |
| 18. #833 | C4 | semidirect |
| 52. C2×M16 | Dic3 | semidirect |
| 54. C22×C8 | Dic3 | semidirect |
| 144. C3 | #1757 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#131 | 2 |
| #5240 | 2 |
| #5237 | 2 |
| #5101 | 2 |
| #4556 | 2 |
| #1757 | 3 |