Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
560 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22598375 | C2 | semidirect |
| 4. #22586768 | C2 | semidirect |
| 6. #22586169 | C2 | semidirect |
| 7. C71×#1995 | C2 | semidirect |
| 209. #1995 | D71 | semidirect |
| 213. C71 | #10016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598375 | 2 |
| #22598344 | 2 |
| #22591626 | 2 |
| #22586768 | 2 |
| #22586764 | 2 |
| #22586169 | 2 |
| C71×#1995 | 2 |
| #10016 | 71 |