Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
262 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 81 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. #4532 | C2 | semidirect |
| 5. #4531 | C2 | semidirect |
| 12. #926 | C4 | semidirect |
| 14. C2×C4×Dic3 | C4 | semidirect |
| 154. C3 | #1827 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Dic3×#41 | 2 |
| C3×#410 | 2 |
| #5237 | 2 |
| #4532 | 2 |
| #4531 | 2 |
| #1827 | 3 |