Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
456 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 116 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 |
|---|---|---|
| 4. C2×#63382 | C2 | semidirect |
| 5. #10588681 | C2 | semidirect |
| 6. C9⋊#338 | C2 | semidirect |
| 7. #10588209 | C2 | semidirect |
| 17. C2×#3674 | C4 | semidirect |
| 18. C2×#3672 | C4 | semidirect |
| 269. C9 | #1902 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63511 | 2 |
| #10589921 | 2 |
| C9×#421 | 2 |
| C2×#63382 | 2 |
| #10588681 | 2 |
| C9⋊#338 | 2 |
| #10588209 | 2 |
| #70399 | 3 |