Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
355 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 355 conjugacy classes of subgroups — too many to draw. Only its 120 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 |
|---|---|---|
| 145. C32 | #1309 | semidirect |
| 174. C3 | C3⋊#1309 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592623 | 2 |
| C3×#4924 | 2 |
| C3⋊#1309 | 3 |