Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
668 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 151 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. #22601481 | C2 | semidirect |
| 2. #22600140 | C2 | semidirect |
| 3. #22590590 | C2 | semidirect |
| 4. #22590460 | C2 | semidirect |
| 5. #22590417 | C2 | semidirect |
| 6. #22590299 | C2 | semidirect |
| 7. #22590222 | C2 | semidirect |
| 8. C71×#2170 | C2 | semidirect |
| 9. #17986804 | C22 | semidirect |
| 12. #17986437 | C22 | semidirect |
| 16. C2×D1136 | C22 | semidirect |
| 17. C2×D1136 | C22 | semidirect |
| 18. #17986376 | C22 | semidirect |
| 20. #17986269 | C22 | semidirect |
| 22. #17986117 | C22 | semidirect |
| 23. #17985829 | C22 | semidirect |
| 24. #17985813 | C22 | semidirect |
| 25. #17985807 | C22 | semidirect |
| 26. #504×C71 | C22 | semidirect |
| 28. #364×C71 | C22 | semidirect |
| 29. #350×C71 | C22 | semidirect |
| 30. C4×C16×C71 | C22 | semidirect |
| 45. Dic568 | D4 | semidirect |
| 47. #14556073 | D4 | semidirect |
| 52. D1136 | D4 | semidirect |
| 150. #2170 | D71 | semidirect |
| 151. C71 | #33858 | semidirect |
| 161. #504 | C2×D71 | semidirect |
| 169. #364 | C2×D71 | semidirect |
| 172. #350 | C2×D71 | semidirect |
| 173. C4×C16 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601481 | 2 |
| #22600140 | 2 |
| #22590590 | 2 |
| #22590460 | 2 |
| #22590417 | 2 |
| #22590299 | 2 |
| #22590222 | 2 |
| C71×#2170 | 2 |
| #33858 | 71 |