Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
690 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 95 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. #19143623 | C2 | semidirect |
| 3. #19133308 | C2 | semidirect |
| 4. #19133308 | C2 | semidirect |
| 5. #19132935 | C2 | semidirect |
| 6. #19132451 | C2 | semidirect |
| 7. C43×#1285 | C2 | semidirect |
| 56. C4⋊(C43⋊C8) | D4 | semidirect |
| 67. C4⋊C8×C43 | D4 | semidirect |
| 220. #1285 | D43 | semidirect |
| 250. C43 | #9457 | semidirect |
| 283. C4⋊C8 | D172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19143623 | 2 |
| #19139537 | 2 |
| #19133308 | 2 |
| #19132935 | 2 |
| #19132451 | 2 |
| C43×#1285 | 2 |
| #9457 | 43 |