Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
578 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×#14582703 | C2 | semidirect |
| 5. #19135457 | C2 | semidirect |
| 6. #19132672 | C2 | semidirect |
| 7. C22×Q32×C43 | C2 | semidirect |
| 186. C22×Q32 | D43 | semidirect |
| 220. C43 | #13329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13063268 | 2 |
| C2×#14583284 | 2 |
| C2×#14582703 | 2 |
| C2×#14582701 | 2 |
| #19135457 | 2 |
| #19132672 | 2 |
| C22×Q32×C43 | 2 |
| #13329 | 43 |