Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
574 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 574 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. #22597421 | C2 | semidirect |
| 4. #22586241 | C2 | semidirect |
| 5. C71×#1801 | C2 | semidirect |
| 142. #1801 | D71 | semidirect |
| 145. C71 | #9398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597421 | 2 |
| #22593339 | 2 |
| #22587009 | 2 |
| #22586241 | 2 |
| C71×#1801 | 2 |
| #9398 | 71 |