Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
276 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 102 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. C9×#334 | C2 | semidirect |
| 4. #10588157 | C2 | semidirect |
| 5. #10588134 | C2 | semidirect |
| 64. C8×C9 | M16 | semidirect |
| 67. C9⋊C8 | M16 | semidirect |
| 72. #334 | D9 | semidirect |
| 159. C9 | #1566 | semidirect |
| 176. C8 | #3663 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10588521 | 2 |
| C4×C8×D9 | 2 |
| C9×#334 | 2 |
| #10588157 | 2 |
| #10588134 | 2 |
| #68529 | 3 |