Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
490 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 109 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. #19147697 | C2 | semidirect |
| 3. #19136311 | C2 | semidirect |
| 4. #19134638 | C2 | semidirect |
| 5. #19132697 | C2 | semidirect |
| 6. #19132696 | C2 | semidirect |
| 7. C43×#2140 | C2 | semidirect |
| 14. #14583149 | C4 | semidirect |
| 43. C2×C43⋊C16 | D4 | semidirect |
| 62. C2×C16×C43 | D4 | semidirect |
| 167. #2140 | D43 | semidirect |
| 195. C43 | #13074 | semidirect |
| 226. C2×C16 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19147697 | 2 |
| #19144239 | 2 |
| #19136311 | 2 |
| #19134638 | 2 |
| #19132697 | 2 |
| #19132696 | 2 |
| C43×#2140 | 2 |
| #13074 | 43 |