Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
668 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 143 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. #22601478 | C2 | semidirect |
| 2. #22600140 | C2 | semidirect |
| 3. #22590590 | C2 | semidirect |
| 4. #22590461 | C2 | semidirect |
| 5. #22590416 | C2 | semidirect |
| 6. #22590298 | C2 | semidirect |
| 7. #22590178 | C2 | semidirect |
| 8. C71×#2178 | C2 | semidirect |
| 10. #17986801 | C22 | semidirect |
| 12. #17986434 | C22 | semidirect |
| 14. C2×D1136 | C22 | semidirect |
| 15. C2×D1136 | C22 | semidirect |
| 17. #17986415 | C22 | semidirect |
| 18. #17986376 | C22 | semidirect |
| 19. #17986270 | C22 | semidirect |
| 23. #17985820 | C22 | semidirect |
| 24. #17985811 | C22 | semidirect |
| 25. #17985782 | C22 | semidirect |
| 27. #443×C71 | C22 | semidirect |
| 28. #368×C71 | C22 | semidirect |
| 29. #359×C71 | C22 | semidirect |
| 30. C4×C16×C71 | C22 | semidirect |
| 58. Q32×C71 | D4 | semidirect |
| 59. SD32×C71 | D4 | semidirect |
| 60. D16×C71 | D4 | semidirect |
| 149. #2178 | D71 | semidirect |
| 151. C71 | #33858 | semidirect |
| 167. #443 | C2×D71 | semidirect |
| 168. #368 | C2×D71 | semidirect |
| 171. #359 | C2×D71 | semidirect |
| 173. C4×C16 | C2×D71 | semidirect |
| 190. Q32 | D284 | semidirect |
| 192. SD32 | D284 | semidirect |
| 197. D16 | D284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601478 | 2 |
| #22600140 | 2 |
| #22590590 | 2 |
| #22590461 | 2 |
| #22590416 | 2 |
| #22590298 | 2 |
| #22590178 | 2 |
| C71×#2178 | 2 |
| #33858 | 71 |