Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
294 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 55 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. #19147728 | C2 | semidirect |
| 2. #19136908 | C2 | semidirect |
| 3. #19136695 | C2 | semidirect |
| 4. #19132783 | C2 | semidirect |
| 5. #19132782 | C2 | semidirect |
| 6. #19132734 | C2 | semidirect |
| 7. C43×#2263 | C2 | semidirect |
| 19. #14582733 | C22 | semidirect |
| 20. #14582727 | C22 | semidirect |
| 23. C2×D16×C43 | C22 | semidirect |
| 26. C43×M64 | C22 | semidirect |
| 38. Dic344 | D4 | semidirect |
| 43. D688 | D4 | semidirect |
| 53. Q32×C43 | D4 | semidirect |
| 57. D16×C43 | D4 | semidirect |
| 141. #2263 | D43 | semidirect |
| 160. C2×D16 | C2×D43 | semidirect |
| 168. M64 | C2×D43 | semidirect |
| 171. C43 | #13667 | semidirect |
| 187. Q32 | C22⋊D43 | semidirect |
| 196. D16 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19147728 | 2 |
| #19136908 | 2 |
| #19136695 | 2 |
| #19132783 | 2 |
| #19132782 | 2 |
| #19132734 | 2 |
| C43×#2263 | 2 |
| #13667 | 43 |