Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
525 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 525 conjugacy classes of subgroups — too many to draw. Only its 168 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. C9×#578 | C2 | semidirect |
| 2. #10589855 | C2 | semidirect |
| 3. #10588875 | C2 | semidirect |
| 4. #10588874 | C2 | semidirect |
| 5. C2×#63388 | C2 | semidirect |
| 6. #10588859 | C2 | semidirect |
| 7. #10588820 | C2 | semidirect |
| 88. #578 | D9 | semidirect |
| 187. C9 | #3417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#578 | 2 |
| #10589855 | 2 |
| #10588875 | 2 |
| #10588874 | 2 |
| C2×#63388 | 2 |
| #10588859 | 2 |
| #10588820 | 2 |
| #84017 | 3 |