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×#63478 | C2 | semidirect |
| 2. #10589827 | C2 | semidirect |
| 3. #10589818 | C2 | semidirect |
| 4. C9×#492 | C2 | semidirect |
| 5. #10588848 | C2 | semidirect |
| 6. #10588765 | C2 | semidirect |
| 7. #10588755 | C2 | semidirect |
| 8. #10588375 | C2 | semidirect |
| 9. C4×C8×D9 | C2 | semidirect |
| 69. C8×D9 | D4 | semidirect |
| 123. #492 | D9 | semidirect |
| 161. C4×C9 | #135 | semidirect |
| 257. C9 | #3147 | semidirect |
| 297. C4 | #63478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63478 | 2 |
| #10589827 | 2 |
| #10589818 | 2 |
| C9×#492 | 2 |
| #10588848 | 2 |
| #10588765 | 2 |
| #10588755 | 2 |
| #10588375 | 2 |
| C4×C8×D9 | 2 |
| #81760 | 3 |