Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
1716 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1716 conjugacy classes of subgroups — too many to draw. Only its 171 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×#14583534 | C2 | semidirect |
| 2. #19145045 | C2 | semidirect |
| 3. #19144687 | C2 | semidirect |
| 4. #19133712 | C2 | semidirect |
| 5. #19133650 | C2 | semidirect |
| 6. #19133037 | C2 | semidirect |
| 7. C43×#1555 | C2 | semidirect |
| 13. #14583449 | C22 | semidirect |
| 18. #14583275 | C22 | semidirect |
| 19. #14583271 | C22 | semidirect |
| 21. #14583190 | C22 | semidirect |
| 22. #14583095 | C22 | semidirect |
| 25. C4×#10621877 | C22 | semidirect |
| 26. #14582626 | C22 | semidirect |
| 28. C43×#432 | C22 | semidirect |
| 29. C43×#331 | C22 | semidirect |
| 43. #13063325 | C23 | semidirect |
| 44. #13063322 | C23 | semidirect |
| 63. C4×C43⋊C8 | C23 | semidirect |
| 70. C4⋊C8×C43 | C23 | semidirect |
| 151. D172 | AGL(1,ℤ/8) | semidirect |
| 183. #1555 | D43 | semidirect |
| 209. #432 | C2×D43 | semidirect |
| 211. #331 | C2×D43 | semidirect |
| 213. C43 | #18524 | semidirect |
| 250. C4⋊C8 | C22×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583534 | 2 |
| #19145045 | 2 |
| #19144687 | 2 |
| #19133712 | 2 |
| #19133650 | 2 |
| #19133037 | 2 |
| C43×#1555 | 2 |
| #18524 | 43 |