Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
506 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 174 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×#97 | C4 | semidirect |
| 16. #63642 | C4 | semidirect |
| 17. #63630 | C4 | semidirect |
| 54. #622 | C42 | semidirect |
| 55. C32×C8 | C42 | semidirect |
| 56. C3⋊(C3⋊C8) | C42 | semidirect |
| 76. #157 | #97 | direct (N × H) |
| 91. #97 | #157 | direct (N × H) |
| 132. C32 | C4×#97 | semidirect |
| 147. C8 | C4×#157 | 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 |
| C42×#157 | 2 |
| #10593723 | 2 |
| C3⋊D3×#97 | 2 |
| C4×#97 | 9 |