Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
243 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 243 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 |
|---|---|---|
| 2. #10588509 | C2 | semidirect |
| 4. C9×#335 | C2 | semidirect |
| 6. #10588160 | C2 | semidirect |
| 7. #10588132 | C2 | semidirect |
| 81. C8×C9 | M16 | semidirect |
| 88. #335 | D9 | semidirect |
| 191. C9 | #1592 | semidirect |
| 211. C8 | #3663 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10588522 | 2 |
| #10588509 | 2 |
| C4×#3664 | 2 |
| C9×#335 | 2 |
| #10588162 | 2 |
| #10588160 | 2 |
| #10588132 | 2 |
| #68565 | 3 |