Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
906 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 906 conjugacy classes of subgroups — too many to draw. Only its 179 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. #19145173 | C2 | semidirect |
| 2. #19145172 | C2 | semidirect |
| 3. #19145022 | C2 | semidirect |
| 4. #19145018 | C2 | semidirect |
| 5. #19134268 | C2 | semidirect |
| 6. #19134266 | C2 | semidirect |
| 7. #19134264 | C2 | semidirect |
| 8. #19134262 | C2 | semidirect |
| 9. #19134260 | C2 | semidirect |
| 10. #322×D43 | C2 | semidirect |
| 11. C43×#1721 | C2 | semidirect |
| 135. C8×D43 | D8 | semidirect |
| 196. #1721 | D43 | semidirect |
| 235. C43 | #19616 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145173 | 2 |
| #19145172 | 2 |
| #19145022 | 2 |
| #19145018 | 2 |
| #19134268 | 2 |
| #19134266 | 2 |
| #19134264 | 2 |
| #19134262 | 2 |
| #19134260 | 2 |
| #322×D43 | 2 |
| C43×#1721 | 2 |
| #19616 | 43 |