Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
325 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 325 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 21. #63551 | C4 | semidirect |
| 242. C32 | #2176 | semidirect |
| 276. C3 | #69338 | semidirect |
| 277. C3 | #70909 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4873 | 2 |
| #10590807 | 2 |
| C2×#63551 | 2 |
| #10589358 | 2 |
| C3×#4490 | 2 |
| #10589117 | 2 |
| #10589103 | 2 |
| #70909 | 3 |
| #69338 | 3 |