Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
470 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 155 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. C2×#14583331 | C2 | semidirect |
| 2. #19136902 | C2 | direct (N × H) |
| 3. C2×#14582739 | C2 | semidirect |
| 4. C2×#14582737 | C2 | semidirect |
| 5. C2×#14582736 | C2 | semidirect |
| 6. C2×#14582734 | C2 | semidirect |
| 7. C22×C43⋊C32 | C2 | semidirect |
| 8. C2×C43×#508 | C2 | semidirect |
| 11. #14583331 | C22 | semidirect |
| 15. #14582739 | C22 | semidirect |
| 16. #14582737 | C22 | semidirect |
| 17. #14582736 | C22 | semidirect |
| 18. #14582734 | C22 | semidirect |
| 21. C2×C43⋊C32 | C22 | semidirect |
| 24. C43×#508 | C22 | semidirect |
| 126. C2×#508 | D43 | semidirect |
| 135. C2×C43 | #2262 | semidirect |
| 143. #508 | C2×D43 | semidirect |
| 158. C43 | C2×#2262 | semidirect |
| 257. C2 | #19136902 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583331 | 2 |
| #19136902 | 2 |
| C2×#14582739 | 2 |
| C2×#14582737 | 2 |
| C2×#14582736 | 2 |
| C2×#14582734 | 2 |
| C22×C43⋊C32 | 2 |
| C2×C43×#508 | 2 |
| C2×#2262 | 43 |