Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
918 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 918 conjugacy classes of subgroups — too many to draw. Only its 179 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×#14583336 | C2 | semidirect |
| 2. #19145024 | C2 | semidirect |
| 3. #493×D43 | C2 | semidirect |
| 4. #19136860 | C2 | semidirect |
| 5. #19136852 | C2 | semidirect |
| 6. #19136845 | C2 | semidirect |
| 7. #19136844 | C2 | semidirect |
| 8. C4×#13063264 | C2 | semidirect |
| 9. C43×#2248 | C2 | semidirect |
| 17. C2×#13063268 | C22 | semidirect |
| 18. C2×D688 | C22 | semidirect |
| 19. C2×#13063266 | C22 | semidirect |
| 22. #14583284 | C22 | semidirect |
| 24. #14583276 | C22 | semidirect |
| 30. #14582674 | C22 | semidirect |
| 31. C4×C43⋊C16 | C22 | semidirect |
| 32. C2×SD32×C43 | C22 | semidirect |
| 33. C43×#494 | C22 | semidirect |
| 35. C4×C16×C43 | C22 | semidirect |
| 64. #13063264 | D4 | semidirect |
| 120. C16×C43 | C2×D4 | semidirect |
| 121. C43⋊C16 | C2×D4 | semidirect |
| 167. C4×C43 | #509 | semidirect |
| 177. #2248 | D43 | semidirect |
| 195. C2×SD32 | C2×D43 | semidirect |
| 201. #494 | C2×D43 | semidirect |
| 212. C4×C16 | C2×D43 | semidirect |
| 213. C43 | #33717 | semidirect |
| 299. C16 | D4×D43 | semidirect |
| 346. C4 | #14583336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583336 | 2 |
| #19145024 | 2 |
| #493×D43 | 2 |
| #19136860 | 2 |
| #19136852 | 2 |
| #19136845 | 2 |
| #19136844 | 2 |
| C4×#13063264 | 2 |
| C43×#2248 | 2 |
| #33717 | 43 |