Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
1068 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1068 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. #19145052 | C2 | semidirect |
| 2. #19144686 | C2 | semidirect |
| 3. #19133740 | C2 | semidirect |
| 4. #19133678 | C2 | semidirect |
| 5. #19133321 | C2 | semidirect |
| 6. #19133038 | C2 | semidirect |
| 7. C2×C43×#555 | C2 | semidirect |
| 11. #14583278 | C22 | semidirect |
| 12. #14583273 | C22 | semidirect |
| 14. #14583189 | C22 | semidirect |
| 15. #14583094 | C22 | semidirect |
| 20. #14582648 | C22 | semidirect |
| 21. D4⋊(C43⋊C8) | C22 | semidirect |
| 162. C2×#555 | D43 | semidirect |
| 196. C43 | #18547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145052 | 2 |
| #19144686 | 2 |
| #19133740 | 2 |
| #19133678 | 2 |
| #19133321 | 2 |
| #19133038 | 2 |
| C2×C43×#555 | 2 |
| #18547 | 43 |