Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
798 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 179 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. #19145157 | C2 | semidirect |
| 2. #19145156 | C2 | semidirect |
| 3. #19145104 | C2 | semidirect |
| 5. #19134226 | C2 | semidirect |
| 6. #19134224 | C2 | semidirect |
| 7. #19134223 | C2 | semidirect |
| 8. #19134220 | C2 | semidirect |
| 9. #19134219 | C2 | semidirect |
| 10. #322×D43 | C2 | semidirect |
| 11. C43×#1716 | C2 | semidirect |
| 130. C8×D43 | SD16 | semidirect |
| 181. #1716 | D43 | semidirect |
| 223. C43 | #19608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145157 | 2 |
| #19145156 | 2 |
| #19145104 | 2 |
| #19145024 | 2 |
| #19134226 | 2 |
| #19134224 | 2 |
| #19134223 | 2 |
| #19134220 | 2 |
| #19134219 | 2 |
| #322×D43 | 2 |
| C43×#1716 | 2 |
| #19608 | 43 |