Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
264 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 264 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 |
|---|---|---|
| 1. C8×D4×C9 | C2 | semidirect |
| 3. #10588691 | C2 | semidirect |
| 4. #10588376 | C2 | semidirect |
| 5. #10588163 | C2 | semidirect |
| 6. #10588158 | C2 | semidirect |
| 7. #10588134 | C2 | semidirect |
| 90. C8×D4 | D9 | semidirect |
| 200. C9 | #1677 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×D4×C9 | 2 |
| #10588698 | 2 |
| #10588691 | 2 |
| #10588376 | 2 |
| #10588163 | 2 |
| #10588158 | 2 |
| #10588134 | 2 |
| #70848 | 3 |