Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
564 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 131 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. #22597251 | C2 | semidirect |
| 2. #22590552 | C2 | semidirect |
| 3. #22590508 | C2 | semidirect |
| 4. #22590413 | C2 | semidirect |
| 5. #22590285 | C2 | semidirect |
| 6. #22590236 | C2 | semidirect |
| 7. #22590152 | C2 | semidirect |
| 8. C71×#3184 | C2 | semidirect |
| 18. #17985821 | C22 | semidirect |
| 19. #17985820 | C22 | semidirect |
| 20. #17985812 | C22 | semidirect |
| 23. #17985777 | C22 | semidirect |
| 25. #498×C71 | C22 | semidirect |
| 26. #493×C71 | C22 | semidirect |
| 31. #442×C71 | C22 | semidirect |
| 80. Dic284 | #41 | semidirect |
| 84. D568 | #41 | semidirect |
| 170. #3184 | D71 | semidirect |
| 178. C71 | #33688 | semidirect |
| 183. #498 | C2×D71 | semidirect |
| 184. #493 | C2×D71 | semidirect |
| 193. #442 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597251 | 2 |
| #22590552 | 2 |
| #22590508 | 2 |
| #22590413 | 2 |
| #22590285 | 2 |
| #22590236 | 2 |
| #22590152 | 2 |
| C71×#3184 | 2 |
| #33688 | 71 |