Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1178 conjugacy classes of subgroups; only the 378 normal subgroups are shown.
This group has 1178 conjugacy classes of subgroups — too many to draw. Only its 378 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 |
|---|---|---|
| 3. C2×#63777 | C2 | direct (N × H) |
| 7. C22×#622 | C4 | semidirect |
| 11. #63777 | C22 | direct (N × H) |
| 21. C2×#622 | C2×C4 | semidirect |
| 43. #622 | C22×C4 | semidirect |
| 57. C22×C32 | #97 | semidirect |
| 86. C2×C32 | C2×#97 | semidirect |
| 111. C32 | C22×#97 | semidirect |
| 129. C22 | #63777 | direct (N × H) |
| 139. C2 | C2×#63777 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#622 | 2 |
| C22×C4×C3⋊Dic3 | 2 |
| C2×#63777 | 2 |
| C22×#97 | 9 |