Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
725 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 725 conjugacy classes of subgroups — too many to draw. Only its 109 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×#63700 | C2 | semidirect |
| 2. C4⋊(#41⋊C9) | C2 | semidirect |
| 3. C4×#41⋊C9 | C2 | semidirect |
| 7. C2×#41⋊C9 | C22 | semidirect |
| 9. C4×Q8⋊C9 | C22 | semidirect |
| 19. #41⋊C9 | D4 | semidirect |
| 23. #3498 | C9 | semidirect |
| 49. Q8⋊C9 | C2×D4 | semidirect |
| 222. C4 | #63700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63700 | 2 |
| C4⋊(#41⋊C9) | 2 |
| C4×#41⋊C9 | 2 |
| C3×#3498 | 3 |
| C9×C4⋊Q8 | 4 |