Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
216 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 1. #10588581 | C2 | semidirect |
| 3. C9×#346 | C2 | semidirect |
| 4. #10588185 | C2 | semidirect |
| 5. #10588140 | C2 | semidirect |
| 61. #346 | D9 | semidirect |
| 124. C9 | #2171 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10588581 | 2 |
| #10588380 | 2 |
| C9×#346 | 2 |
| #10588185 | 2 |
| #10588140 | 2 |
| #69076 | 3 |