Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
573 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 573 conjugacy classes of subgroups — too many to draw. Only its 104 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. C22×C9×D8 | C2 | semidirect |
| 2. C2×#63495 | C2 | semidirect |
| 3. C2×#63391 | C2 | semidirect |
| 4. #10588791 | C2 | semidirect |
| 5. #10588227 | C2 | semidirect |
| 87. C22×D8 | D9 | semidirect |
| 206. C9 | #2018 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C9×D8 | 2 |
| C2×#63495 | 2 |
| C2×#63391 | 2 |
| #10588791 | 2 |
| #10588227 | 2 |
| #72046 | 3 |