Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
558 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 558 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. #19145182 | C2 | semidirect |
| 3. #19136875 | C2 | semidirect |
| 4. #19136850 | C2 | semidirect |
| 5. #19136823 | C2 | semidirect |
| 6. #19136690 | C2 | semidirect |
| 7. #19136450 | C2 | semidirect |
| 8. C4×C16×D43 | C2 | semidirect |
| 9. C43×#2240 | C2 | semidirect |
| 113. C43⋊C16 | #41 | semidirect |
| 135. C4×D43 | SD32 | semidirect |
| 166. #2240 | D43 | semidirect |
| 200. C43 | #33736 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145182 | 2 |
| #19145172 | 2 |
| #19136875 | 2 |
| #19136850 | 2 |
| #19136823 | 2 |
| #19136690 | 2 |
| #19136450 | 2 |
| C4×C16×D43 | 2 |
| C43×#2240 | 2 |
| #33736 | 43 |