Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
234 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 4. #19132659 | C2 | semidirect |
| 5. #19132653 | C2 | semidirect |
| 6. #19132644 | C2 | semidirect |
| 7. C43×#1707 | C2 | semidirect |
| 87. C8×C43 | SD32 | semidirect |
| 106. #1707 | D43 | semidirect |
| 130. C43 | #12420 | semidirect |
| 196. C8 | #13063268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19136739 | 2 |
| #19136637 | 2 |
| C8×D344 | 2 |
| #19132659 | 2 |
| #19132653 | 2 |
| #19132644 | 2 |
| C43×#1707 | 2 |
| #12420 | 43 |