Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
490 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 158 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 |
|---|---|---|
| 12. #63777 | C4 | semidirect |
| 13. #63767 | C4 | semidirect |
| 14. C8×#157 | C4 | semidirect |
| 15. C32×C4×C8 | C4 | semidirect |
| 16. C8×C3⋊Dic3 | C4 | semidirect |
| 17. C8×C3⋊Dic3 | C4 | semidirect |
| 18. C4×C3⋊(C3⋊C8) | C4 | semidirect |
| 96. C4×C8 | #157 | semidirect |
| 138. C32 | #1726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63767 | 2 |
| C2×C8×#157 | 2 |
| #10593733 | 2 |
| #10593723 | 2 |
| C4×C8×C3⋊D3 | 2 |
| #1726 | 9 |