Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
300 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 72 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. #10588767 | C2 | semidirect |
| 4. #10588758 | C2 | semidirect |
| 6. #10588160 | C2 | semidirect |
| 7. #10588159 | C2 | semidirect |
| 220. C9 | #1650 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589644 | 2 |
| C9×#461 | 2 |
| #10588767 | 2 |
| #10588758 | 2 |
| D4⋊(C9⋊C8) | 2 |
| #10588160 | 2 |
| #10588159 | 2 |
| #71049 | 3 |