Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
401 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 401 conjugacy classes of subgroups — too many to draw. Only its 116 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 |
|---|---|---|
| 172. C32 | #1716 | semidirect |
| 196. C3 | #68095 | semidirect |
| 197. C3 | #71299 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592379 | 2 |
| C3×#4699 | 2 |
| #10590303 | 2 |
| #10590288 | 2 |
| C3×#4455 | 2 |
| #71299 | 3 |
| #68095 | 3 |