Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
370 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 15. C32×#107 | C4 | semidirect |
| 16. #63645 | C4 | semidirect |
| 17. #63634 | C4 | semidirect |
| 62. C32×C8 | C4⋊C4 | semidirect |
| 63. C3⋊(C3⋊C8) | C4⋊C4 | semidirect |
| 99. #107 | #157 | semidirect |
| 151. C32 | #1943 | semidirect |
| 171. C8 | C4⋊#157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63768 | 2 |
| C2×#63767 | 2 |
| #10593759 | 2 |
| C3⋊D3×#107 | 2 |
| #10590163 | 2 |
| #1943 | 9 |