Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
306 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 82 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. #10588799 | C2 | semidirect |
| 5. #10588232 | C2 | semidirect |
| 6. #10588210 | C2 | semidirect |
| 7. #10588209 | C2 | semidirect |
| 210. C9 | #2081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#418 | 2 |
| #10588896 | 2 |
| C2×#63391 | 2 |
| #10588799 | 2 |
| #10588232 | 2 |
| #10588210 | 2 |
| #10588209 | 2 |
| #70322 | 3 |