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×#63474 | C2 | semidirect |
| 2. #10589818 | C2 | semidirect |
| 3. C9×#493 | C2 | semidirect |
| 4. #10588835 | C2 | semidirect |
| 5. #10588753 | C2 | semidirect |
| 6. C4×C8×D9 | C2 | semidirect |
| 7. #10588365 | C2 | semidirect |
| 48. C8×D9 | D4 | semidirect |
| 86. #493 | D9 | semidirect |
| 113. C4×C9 | #135 | semidirect |
| 182. C9 | #3147 | semidirect |
| 211. C4 | #63474 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63474 | 2 |
| #10589818 | 2 |
| C9×#493 | 2 |
| #10588835 | 2 |
| #10588753 | 2 |
| C4×C8×D9 | 2 |
| #10588365 | 2 |
| #81782 | 3 |