Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
306 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 3. #10588799 | C2 | semidirect |
| 5. C9×#344 | C2 | semidirect |
| 6. #10588232 | C2 | semidirect |
| 7. #10588210 | C2 | semidirect |
| 91. #344 | D9 | semidirect |
| 210. C9 | #2081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10588813 | 2 |
| C2×#63383 | 2 |
| #10588799 | 2 |
| #10588682 | 2 |
| C9×#344 | 2 |
| #10588232 | 2 |
| #10588210 | 2 |
| #69021 | 3 |