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. #19136840 | C2 | semidirect |
| 4. #19136838 | C2 | semidirect |
| 5. #19136837 | C2 | semidirect |
| 6. #19136828 | C2 | semidirect |
| 7. #19136306 | C2 | semidirect |
| 8. #19136188 | C2 | semidirect |
| 9. C43×#2245 | C2 | semidirect |
| 148. #2245 | 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 |
| #19145024 | 2 |
| #19136840 | 2 |
| #19136838 | 2 |
| #19136837 | 2 |
| #19136828 | 2 |
| #19136306 | 2 |
| #19136188 | 2 |
| C43×#2245 | 2 |
| #33708 | 43 |