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. #19134481 | C2 | semidirect |
| 6. #19132711 | C2 | semidirect |
| 7. C43×#1384 | C2 | semidirect |
| 11. #14583010 | C4 | semidirect |
| 12. #14583005 | C4 | semidirect |
| 18. #14582708 | C4 | semidirect |
| 19. #14582707 | C4 | semidirect |
| 42. #13063265 | C2×C4 | semidirect |
| 45. #13063261 | C2×C4 | semidirect |
| 57. C2×C16×C43 | C2×C4 | semidirect |
| 61. #106×C43 | C2×C4 | semidirect |
| 153. #1384 | D43 | semidirect |
| 176. C43 | #12649 | semidirect |
| 201. C2×C16 | C4×D43 | semidirect |
| 207. #106 | C4×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19143395 | 2 |
| #19136330 | 2 |
| #19136324 | 2 |
| C2×#14582676 | 2 |
| #19134481 | 2 |
| #19132711 | 2 |
| C43×#1384 | 2 |
| #12649 | 43 |