Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1554 conjugacy classes of subgroups; only the 374 normal subgroups are shown.
This group has 1554 conjugacy classes of subgroups — too many to draw. Only its 374 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. C23×Q8×C9 | C2 | semidirect |
| 3. #10588911 | C2 | direct (N × H) |
| 4. C2×C9⋊#95 | C2 | semidirect |
| 8. C22×Q8×C9 | C22 | semidirect |
| 13. C9⋊#95 | C22 | semidirect |
| 21. C23×D9 | Q8 | semidirect |
| 50. C22×D9 | C2×Q8 | semidirect |
| 58. C23×Q8 | D9 | semidirect |
| 90. C22×Q8 | C2×D9 | semidirect |
| 113. C2×C9 | #393 | semidirect |
| 144. C9 | C2×#393 | semidirect |
| 181. C2 | #10588911 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Q8×C9 | 2 |
| C22×(C2×D9)⋊C4 | 2 |
| #10588911 | 2 |
| C2×C9⋊#95 | 2 |
| C2×#5231 | 3 |