Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
212 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 212 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 |
|---|---|---|
| 16. #824 | C4 | semidirect |
| 181. C3 | #1930 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#824 | 2 |
| #5121 | 2 |
| #5120 | 2 |
| C2×#816 | 2 |
| #5101 | 2 |
| C3×#341 | 2 |
| #4554 | 2 |
| #1930 | 3 |