Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
514 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 89 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. #19143231 | C2 | semidirect |
| 3. #19133038 | C2 | semidirect |
| 4. #19132927 | C2 | semidirect |
| 5. #19132461 | C2 | semidirect |
| 6. #19132460 | C2 | semidirect |
| 7. C43×#1490 | C2 | semidirect |
| 54. C4×C43⋊C8 | D4 | semidirect |
| 75. C4×C8×C43 | D4 | semidirect |
| 217. #1490 | D43 | semidirect |
| 251. C43 | #9494 | semidirect |
| 290. C4×C8 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19143231 | 2 |
| #19140155 | 2 |
| #19133038 | 2 |
| #19132927 | 2 |
| #19132461 | 2 |
| #19132460 | 2 |
| C43×#1490 | 2 |
| #9494 | 43 |