Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
654 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 85 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. #19145598 | C2 | semidirect |
| 2. #19144694 | C2 | semidirect |
| 3. #19135538 | C2 | semidirect |
| 4. #19133193 | C2 | semidirect |
| 5. #19133038 | C2 | semidirect |
| 6. #19132451 | C2 | semidirect |
| 37. #13063325 | D4 | semidirect |
| 38. #13063325 | D4 | semidirect |
| 47. C4⋊(C43⋊C8) | D4 | semidirect |
| 56. #13063236 | D4 | semidirect |
| 260. C43 | #10008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145598 | 2 |
| #19144694 | 2 |
| #19135538 | 2 |
| #19133193 | 2 |
| #19133038 | 2 |
| #19132451 | 2 |
| C43×#2540 | 2 |
| #10008 | 43 |