Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
706 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 706 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. #19143635 | C2 | semidirect |
| 3. #19134584 | C2 | semidirect |
| 4. #19133264 | C2 | semidirect |
| 5. #19133262 | C2 | semidirect |
| 6. #19132498 | C2 | semidirect |
| 7. C43×#1303 | C2 | semidirect |
| 50. C4⋊(C43⋊C8) | D4 | semidirect |
| 61. C4⋊C8×C43 | D4 | semidirect |
| 196. #1303 | D43 | semidirect |
| 222. C43 | #9405 | semidirect |
| 254. C4⋊C8 | D172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19143635 | 2 |
| #19139537 | 2 |
| #19134584 | 2 |
| #19133264 | 2 |
| #19133262 | 2 |
| #19132498 | 2 |
| C43×#1303 | 2 |
| #9405 | 43 |