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. C9×#380 | C2 | semidirect |
| 3. C2×#63389 | C2 | semidirect |
| 4. #10588129 | C2 | semidirect |
| 8. C22×D36 | C4 | semidirect |
| 13. #63492 | C4 | semidirect |
| 16. C2×C4⋊Dic9 | C4 | semidirect |
| 18. C9×#95 | C22 | semidirect |
| 20. #63389 | C22 | semidirect |
| 101. #380 | D9 | semidirect |
| 166. #95 | 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 |
| C9×#380 | 2 |
| C2×#63389 | 2 |
| #10588129 | 2 |
| #69509 | 3 |