Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
785 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 785 conjugacy classes of subgroups — too many to draw. Only its 172 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×#63808 | C2 | semidirect |
| 2. C2×#63626 | C2 | semidirect |
| 3. C2×C3×Dic24 | C2 | semidirect |
| 4. C2×C3×D3×C16 | C2 | semidirect |
| 5. C2×#63549 | C2 | semidirect |
| 6. #10590243 | C2 | direct (N × H) |
| 15. #63808 | C22 | semidirect |
| 17. #63626 | C22 | semidirect |
| 19. C3×Dic24 | C22 | semidirect |
| 20. C3×D3×C16 | C22 | semidirect |
| 21. #63549 | C22 | semidirect |
| 28. C2×Dic24 | D3 | semidirect |
| 34. C2×D3×C16 | D3 | semidirect |
| 77. Dic24 | C2×D3 | semidirect |
| 82. D3×C16 | C2×D3 | semidirect |
| 206. C2×C32 | #508 | semidirect |
| 251. C32 | C2×#508 | semidirect |
| 271. C2×C3 | #4904 | semidirect |
| 272. C2×C3 | #4919 | semidirect |
| 289. C3 | C2×#4904 | semidirect |
| 290. C3 | C2×#4919 | semidirect |
| 293. C2 | #10590243 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63808 | 2 |
| C2×#63626 | 2 |
| C2×C3×Dic24 | 2 |
| C2×C3×D3×C16 | 2 |
| C2×#63549 | 2 |
| #10590243 | 2 |
| C2×#4919 | 3 |
| C2×#4904 | 3 |