Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
1152 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 1152 conjugacy classes of subgroups — too many to draw. Only its 155 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×#14583641 | C2 | semidirect |
| 2. #19145578 | C2 | semidirect |
| 3. #19133899 | C2 | semidirect |
| 4. #19133883 | C2 | semidirect |
| 5. #19133219 | C2 | semidirect |
| 6. #19133192 | C2 | semidirect |
| 7. C43×#3153 | C2 | semidirect |
| 16. #14583286 | C22 | semidirect |
| 17. #14583261 | C22 | semidirect |
| 21. #14582956 | C22 | semidirect |
| 22. #14582639 | C22 | semidirect |
| 23. #14582638 | C22 | semidirect |
| 26. C43×#532 | C22 | semidirect |
| 28. C43×#497 | C22 | semidirect |
| 29. C43×#496 | C22 | semidirect |
| 31. C4×M16×C43 | C22 | semidirect |
| 60. #13063236 | C23 | semidirect |
| 71. C4⋊Q8×C43 | C23 | semidirect |
| 72. #127×C43 | C23 | semidirect |
| 81. #97×C43 | C23 | semidirect |
| 203. #3153 | D43 | semidirect |
| 219. #532 | C2×D43 | semidirect |
| 226. #497 | C2×D43 | semidirect |
| 228. #496 | C2×D43 | semidirect |
| 235. C4×M16 | C2×D43 | semidirect |
| 238. C43 | #18992 | semidirect |
| 256. C4⋊Q8 | C22×D43 | semidirect |
| 257. #127 | C22×D43 | semidirect |
| 288. #97 | C22×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583641 | 2 |
| #19145578 | 2 |
| #19133899 | 2 |
| #19133883 | 2 |
| #19133219 | 2 |
| #19133192 | 2 |
| C43×#3153 | 2 |
| #18992 | 43 |