Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 123 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. C2×#14582676 | C2 | semidirect |
| 5. #19134482 | C2 | semidirect |
| 6. #19132696 | C2 | semidirect |
| 7. C43×#1389 | C2 | semidirect |
| 11. #14583010 | C4 | semidirect |
| 12. #14583005 | C4 | semidirect |
| 18. #14582710 | C4 | semidirect |
| 19. #14582705 | C4 | semidirect |
| 43. C2×C43⋊C16 | C2×C4 | semidirect |
| 45. #13063257 | C2×C4 | semidirect |
| 56. M32×C43 | C2×C4 | semidirect |
| 59. #108×C43 | C2×C4 | semidirect |
| 152. #1389 | D43 | semidirect |
| 176. C43 | #12649 | semidirect |
| 199. M32 | C4×D43 | semidirect |
| 203. #108 | C4×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19143395 | 2 |
| #19136332 | 2 |
| #19136322 | 2 |
| C2×#14582676 | 2 |
| #19134482 | 2 |
| #19132696 | 2 |
| C43×#1389 | 2 |
| #12649 | 43 |