Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 20. #869 | C4 | semidirect |
| 198. C3 | #1886 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5516 | 2 |
| C2×#869 | 2 |
| C2×#824 | 2 |
| #5120 | 2 |
| #5004 | 2 |
| C3×#339 | 2 |
| #4523 | 2 |
| #1886 | 3 |