Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
277 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 277 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 |
|---|---|---|
| 4. #10589138 | C2 | semidirect |
| 5. #10589129 | C2 | semidirect |
| 196. C32 | #2239 | semidirect |
| 227. C3 | #70724 | semidirect |
| 228. C3 | #71090 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5137 | 2 |
| C3×#5125 | 2 |
| #10589419 | 2 |
| #10589138 | 2 |
| #10589129 | 2 |
| #71090 | 3 |
| #70724 | 3 |