Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
590 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 151 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. #499×D43 | C2 | semidirect |
| 3. #19136842 | C2 | semidirect |
| 4. #19136841 | C2 | semidirect |
| 5. #19136836 | C2 | semidirect |
| 6. #19136825 | C2 | semidirect |
| 7. #19136304 | C2 | semidirect |
| 8. #19136188 | C2 | semidirect |
| 9. C43×#2244 | C2 | semidirect |
| 150. #2244 | D43 | semidirect |
| 183. C43 | #33708 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #499×D43 | 2 |
| #19145022 | 2 |
| #19136842 | 2 |
| #19136841 | 2 |
| #19136836 | 2 |
| #19136825 | 2 |
| #19136304 | 2 |
| #19136188 | 2 |
| C43×#2244 | 2 |
| #33708 | 43 |