Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
730 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 162 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 |
|---|---|---|
| 1. C2×#64289 | C2 | semidirect |
| 3. C2×#63785 | C2 | semidirect |
| 4. #10593788 | C2 | direct (N × H) |
| 5. C2×#63770 | C2 | semidirect |
| 6. C2×#63767 | C2 | semidirect |
| 9. #64289 | C22 | semidirect |
| 15. C2×C32×Q16 | C4 | semidirect |
| 16. C2×#3755 | C4 | semidirect |
| 17. #64128 | C4 | semidirect |
| 19. C2×#3745 | C4 | semidirect |
| 21. #63785 | C22 | semidirect |
| 22. #63770 | C22 | semidirect |
| 23. #63767 | C22 | semidirect |
| 45. C32×Q16 | C2×C4 | semidirect |
| 47. #3755 | C2×C4 | semidirect |
| 49. #3745 | C2×C4 | semidirect |
| 120. C2×Q16 | #157 | semidirect |
| 153. C2×C32 | #444 | semidirect |
| 168. Q16 | C2×#157 | semidirect |
| 196. C32 | C2×#444 | semidirect |
| 241. C2 | #10593788 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64289 | 2 |
| C2×#64128 | 2 |
| C2×#63785 | 2 |
| #10593788 | 2 |
| C2×#63770 | 2 |
| C2×#63767 | 2 |
| C2×#444 | 9 |