Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
470 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 2. #22596998 | C2 | semidirect |
| 5. #22586246 | C2 | semidirect |
| 6. #22586228 | C2 | semidirect |
| 7. C71×#1825 | C2 | semidirect |
| 16. #17986042 | C4 | semidirect |
| 17. #17986042 | C4 | semidirect |
| 19. #17986003 | C4 | semidirect |
| 20. #17986003 | C4 | semidirect |
| 225. #1825 | D71 | semidirect |
| 230. C71 | #9348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598280 | 2 |
| #22596998 | 2 |
| #22586907 | 2 |
| #22586699 | 2 |
| #22586246 | 2 |
| #22586228 | 2 |
| C71×#1825 | 2 |
| #9348 | 71 |