Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
506 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 4. #19132608 | C2 | semidirect |
| 5. #19132607 | C2 | semidirect |
| 6. #19132606 | C2 | semidirect |
| 7. C43×#1348 | C2 | semidirect |
| 8. C2×Q16×D43 | C4 | semidirect |
| 13. #14583141 | C4 | semidirect |
| 17. #14583137 | C4 | semidirect |
| 18. #107×D43 | C4 | semidirect |
| 30. C2×Dic172 | C2×C4 | semidirect |
| 53. #13063259 | C2×C4 | semidirect |
| 58. C2×Q16×C43 | C2×C4 | semidirect |
| 63. #107×C43 | C2×C4 | semidirect |
| 190. #1348 | D43 | direct (N × H) |
| 197. D43 | #1348 | direct (N × H) |
| 217. C43 | C2×#1348 | semidirect |
| 224. C2×Q16 | C4×D43 | semidirect |
| 251. #107 | C4×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #467×D43 | 2 |
| C22⋊C16×D43 | 2 |
| #340×D43 | 2 |
| #19132608 | 2 |
| #19132607 | 2 |
| #19132606 | 2 |
| C43×#1348 | 2 |
| C2×#1348 | 43 |