Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
406 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 63 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. #19146204 | C2 | semidirect |
| 2. #19136862 | C2 | semidirect |
| 3. #19136631 | C2 | semidirect |
| 4. #19134075 | C2 | semidirect |
| 5. #19132561 | C2 | semidirect |
| 6. #19132552 | C2 | semidirect |
| 7. C43×#1360 | C2 | semidirect |
| 13. #14583276 | C22 | semidirect |
| 22. #14582675 | C22 | semidirect |
| 25. C43×C4⋊C16 | C22 | semidirect |
| 26. C43×#334 | C22 | semidirect |
| 109. D344 | D8 | semidirect |
| 177. #1360 | D43 | semidirect |
| 201. C4⋊C16 | C2×D43 | semidirect |
| 204. #334 | C2×D43 | semidirect |
| 206. C43 | #12324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19146204 | 2 |
| #19136862 | 2 |
| #19136631 | 2 |
| #19134075 | 2 |
| #19132561 | 2 |
| #19132552 | 2 |
| C43×#1360 | 2 |
| #12324 | 43 |