Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
572 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 131 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. #19145169 | C2 | semidirect |
| 2. #19136741 | C2 | semidirect |
| 3. #19136740 | C2 | semidirect |
| 4. #19136698 | C2 | semidirect |
| 5. #19136696 | C2 | semidirect |
| 6. #19136629 | C2 | semidirect |
| 7. #19136628 | C2 | semidirect |
| 8. #19136350 | C2 | semidirect |
| 9. C43×#2218 | C2 | semidirect |
| 153. #2218 | D43 | semidirect |
| 187. C43 | #33819 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145169 | 2 |
| #19136741 | 2 |
| #19136740 | 2 |
| #19136698 | 2 |
| #19136696 | 2 |
| #19136629 | 2 |
| #19136628 | 2 |
| #19136350 | 2 |
| C43×#2218 | 2 |
| #33819 | 43 |