Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
256 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 186. C3 | #2047 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#216 | 2 |
| C3×#419 | 2 |
| C2×#836 | 2 |
| C2×#824 | 2 |
| #5004 | 2 |
| #4999 | 2 |
| #4558 | 2 |
| #2047 | 3 |