Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
291 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 291 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 230. C32 | #2229 | semidirect |
| 262. C3 | #69212 | semidirect |
| 263. C3 | #69336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592577 | 2 |
| #10590818 | 2 |
| C3×#4492 | 2 |
| C3×#4489 | 2 |
| #10589141 | 2 |
| #10589133 | 2 |
| #10589118 | 2 |
| #69336 | 3 |
| #69212 | 3 |