Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
668 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 135 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. #22601477 | C2 | semidirect |
| 2. #22600139 | C2 | semidirect |
| 3. #22590457 | C2 | semidirect |
| 4. #22590413 | C2 | semidirect |
| 5. #22590296 | C2 | semidirect |
| 6. #22590222 | C2 | semidirect |
| 7. #22590178 | C2 | semidirect |
| 8. C71×#2246 | C2 | semidirect |
| 10. #17986800 | C22 | semidirect |
| 11. #17986435 | C22 | semidirect |
| 16. #17986415 | C22 | semidirect |
| 18. #17986266 | C22 | semidirect |
| 21. #17986117 | C22 | semidirect |
| 22. #17985829 | C22 | semidirect |
| 23. #17985820 | C22 | semidirect |
| 24. #17985812 | C22 | semidirect |
| 25. #17985807 | C22 | semidirect |
| 26. #17985782 | C22 | semidirect |
| 27. C2×D16×C71 | C22 | semidirect |
| 28. C2×D16×C71 | C22 | semidirect |
| 29. #493×C71 | C22 | semidirect |
| 30. C4×C16×C71 | C22 | semidirect |
| 44. Dic568 | D4 | semidirect |
| 45. #14556073 | D4 | semidirect |
| 47. D1136 | D4 | semidirect |
| 145. #2246 | D71 | semidirect |
| 151. C71 | #33858 | semidirect |
| 159. C2×D16 | C2×D71 | semidirect |
| 160. C2×D16 | C2×D71 | semidirect |
| 162. #493 | 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 |
|---|---|
| #22601477 | 2 |
| #22600139 | 2 |
| #22590457 | 2 |
| #22590413 | 2 |
| #22590296 | 2 |
| #22590222 | 2 |
| #22590178 | 2 |
| C71×#2246 | 2 |
| #33858 | 71 |