Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
574 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22597420 | C2 | semidirect |
| 3. #22588333 | C2 | semidirect |
| 6. #22586243 | C2 | semidirect |
| 7. C71×#1303 | C2 | semidirect |
| 188. #1303 | D71 | semidirect |
| 189. C71 | #9398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597420 | 2 |
| #22593342 | 2 |
| #22588333 | 2 |
| #22587009 | 2 |
| #22587007 | 2 |
| #22586243 | 2 |
| C71×#1303 | 2 |
| #9398 | 71 |