Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
232 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 75 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. #4964 | C2 | semidirect |
| 6. #4552 | C2 | semidirect |
| 7. #4530 | C2 | semidirect |
| 18. #833 | C4 | semidirect |
| 194. C3 | #1931 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#102 | 2 |
| C2×#833 | 2 |
| #5215 | 2 |
| #5101 | 2 |
| #4964 | 2 |
| #4552 | 2 |
| #4530 | 2 |
| #1931 | 3 |