Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
216 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 64 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. C9×#473 | C2 | semidirect |
| 2. C2×#63387 | C2 | semidirect |
| 4. #10588820 | C2 | semidirect |
| 5. #10588242 | C2 | semidirect |
| 6. #10588172 | C2 | semidirect |
| 7. #10588170 | C2 | semidirect |
| 85. #473 | D9 | semidirect |
| 181. C9 | #2223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#473 | 2 |
| C2×#63387 | 2 |
| #10588823 | 2 |
| #10588820 | 2 |
| #10588242 | 2 |
| #10588172 | 2 |
| #10588170 | 2 |
| #71097 | 3 |