Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
322 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 4. #22586323 | C2 | semidirect |
| 5. #22586322 | C2 | semidirect |
| 6. #22586321 | C2 | semidirect |
| 7. C71×#1338 | C2 | semidirect |
| 150. #1338 | D71 | semidirect |
| 151. C71 | #11612 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597271 | 2 |
| #22590094 | 2 |
| #346×D71 | 2 |
| #22586323 | 2 |
| #22586322 | 2 |
| #22586321 | 2 |
| C71×#1338 | 2 |
| #11612 | 71 |