Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
452 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 127 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. #19147745 | C2 | semidirect |
| 2. #19147744 | C2 | semidirect |
| 3. #19136915 | C2 | semidirect |
| 4. #19136914 | C2 | semidirect |
| 5. #19136911 | C2 | semidirect |
| 6. #19136903 | C2 | semidirect |
| 7. #19136902 | C2 | semidirect |
| 8. C2×#14582739 | C2 | semidirect |
| 9. Q64×D43 | C2 | semidirect |
| 10. #19136890 | C2 | semidirect |
| 11. C43×#2264 | C2 | semidirect |
| 160. #2264 | D43 | semidirect |
| 200. C43 | #33984 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19147745 | 2 |
| #19147744 | 2 |
| #19136915 | 2 |
| #19136914 | 2 |
| #19136911 | 2 |
| #19136903 | 2 |
| #19136902 | 2 |
| C2×#14582739 | 2 |
| Q64×D43 | 2 |
| #19136890 | 2 |
| C43×#2264 | 2 |
| #33984 | 43 |