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. #19145153 | C2 | semidirect |
| 2. #19145152 | C2 | semidirect |
| 3. #19145104 | C2 | semidirect |
| 5. #19134229 | C2 | semidirect |
| 6. #19134228 | C2 | semidirect |
| 7. #19134221 | C2 | semidirect |
| 8. #19134216 | C2 | semidirect |
| 9. #19134215 | C2 | semidirect |
| 10. #322×D43 | C2 | semidirect |
| 11. C43×#1715 | C2 | semidirect |
| 130. C8×D43 | SD16 | semidirect |
| 183. #1715 | 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 |
|---|---|
| #19145153 | 2 |
| #19145152 | 2 |
| #19145104 | 2 |
| #19145022 | 2 |
| #19134229 | 2 |
| #19134228 | 2 |
| #19134221 | 2 |
| #19134216 | 2 |
| #19134215 | 2 |
| #322×D43 | 2 |
| C43×#1715 | 2 |
| #19608 | 43 |