Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
858 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 858 conjugacy classes of subgroups — too many to draw. Only its 178 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×#63481 | C2 | semidirect |
| 2. #10589827 | C2 | semidirect |
| 3. C9×#494 | C2 | semidirect |
| 4. #10588871 | C2 | semidirect |
| 5. #10588770 | C2 | semidirect |
| 6. #10588377 | C2 | semidirect |
| 7. C4×C8×D9 | C2 | semidirect |
| 49. C8×D9 | D4 | semidirect |
| 85. #494 | D9 | semidirect |
| 114. C4×C9 | #135 | semidirect |
| 182. C9 | #3147 | semidirect |
| 211. C4 | #63481 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63481 | 2 |
| #10589827 | 2 |
| C9×#494 | 2 |
| #10588871 | 2 |
| #10588770 | 2 |
| #10588377 | 2 |
| C4×C8×D9 | 2 |
| #81799 | 3 |