Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
240 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 4. #10588360 | C2 | semidirect |
| 5. #10588161 | C2 | semidirect |
| 6. #10588158 | C2 | semidirect |
| 7. #10588135 | C2 | semidirect |
| 81. C8×C9 | SD16 | semidirect |
| 189. C9 | #1691 | semidirect |
| 208. C8 | #3672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#436 | 2 |
| #10588695 | 2 |
| #10588691 | 2 |
| #10588360 | 2 |
| #10588161 | 2 |
| #10588158 | 2 |
| #10588135 | 2 |
| #70872 | 3 |