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×#14583333 | C2 | semidirect |
| 2. #19145022 | C2 | semidirect |
| 3. #493×D43 | C2 | semidirect |
| 4. #19136858 | C2 | semidirect |
| 5. #19136851 | C2 | semidirect |
| 6. #19136850 | C2 | semidirect |
| 7. #19136844 | C2 | semidirect |
| 8. C4×#13063264 | C2 | semidirect |
| 9. C43×#2246 | C2 | semidirect |
| 17. C2×#13063270 | C22 | semidirect |
| 18. C2×#13063269 | C22 | semidirect |
| 19. C2×#13063266 | C22 | semidirect |
| 22. #14583282 | C22 | semidirect |
| 23. #14583279 | C22 | semidirect |
| 30. #14582674 | C22 | semidirect |
| 31. C4×C43⋊C16 | C22 | semidirect |
| 32. C2×D16×C43 | C22 | semidirect |
| 34. C43×#493 | C22 | semidirect |
| 35. C4×C16×C43 | C22 | semidirect |
| 64. #13063264 | D4 | semidirect |
| 120. C16×C43 | C2×D4 | semidirect |
| 121. C43⋊C16 | C2×D4 | semidirect |
| 166. C4×C43 | #509 | semidirect |
| 179. #2246 | D43 | semidirect |
| 197. C2×D16 | C2×D43 | semidirect |
| 207. #493 | C2×D43 | semidirect |
| 212. C4×C16 | C2×D43 | semidirect |
| 213. C43 | #33717 | semidirect |
| 299. C16 | D4×D43 | semidirect |
| 346. C4 | #14583333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583333 | 2 |
| #19145022 | 2 |
| #493×D43 | 2 |
| #19136858 | 2 |
| #19136851 | 2 |
| #19136850 | 2 |
| #19136844 | 2 |
| C4×#13063264 | 2 |
| C43×#2246 | 2 |
| #33717 | 43 |