Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
328 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 205 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 |
|---|---|---|
| 12. C3×C4×C8 | C4 | semidirect |
| 14. #815 | C4 | semidirect |
| 15. C8×Dic3 | C4 | semidirect |
| 16. #803 | C4 | semidirect |
| 44. C4×C8 | Dic3 | semidirect |
| 103. C3 | #1726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×C8 | 2 |
| C2×#815 | 2 |
| C2×C8×Dic3 | 2 |
| #4932 | 2 |
| C2×#803 | 2 |
| #1726 | 3 |