Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
510 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 124 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 |
|---|---|---|
| 2. C2×C9×C22⋊C8 | C2 | semidirect |
| 3. #10588892 | C2 | semidirect |
| 4. #10588147 | C2 | semidirect |
| 8. C22×D36 | C4 | semidirect |
| 13. #63492 | C4 | semidirect |
| 17. C2×C4⋊Dic9 | C4 | semidirect |
| 19. C9×C22⋊C8 | C22 | semidirect |
| 20. C9⋊#95 | C22 | semidirect |
| 100. C2×C22⋊C8 | D9 | semidirect |
| 165. C22⋊C8 | C2×D9 | semidirect |
| 256. C9 | #1519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63492 | 2 |
| C2×C9×C22⋊C8 | 2 |
| #10588892 | 2 |
| #10588147 | 2 |
| #69944 | 3 |