Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
537 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 537 conjugacy classes of subgroups — too many to draw. Only its 154 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. #10588763 | C2 | semidirect |
| 4. #10588745 | C2 | semidirect |
| 7. #10588706 | C2 | semidirect |
| 8. C4×#3674 | C2 | semidirect |
| 250. C9 | #3127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#541 | 2 |
| #10589618 | 2 |
| #10588763 | 2 |
| #10588745 | 2 |
| #10588726 | 2 |
| #10588725 | 2 |
| #10588706 | 2 |
| C4×#3674 | 2 |
| #10588678 | 2 |
| #83451 | 3 |