Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
494 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. #22589161 | C2 | semidirect |
| 5. #22586200 | C2 | semidirect |
| 6. #22586170 | C2 | semidirect |
| 7. C71×#1546 | C2 | semidirect |
| 10. #17986402 | C4 | semidirect |
| 11. #17986347 | C4 | semidirect |
| 185. #1546 | D71 | semidirect |
| 189. C71 | #9291 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599461 | 2 |
| #22597057 | 2 |
| #22589161 | 2 |
| #22586901 | 2 |
| #22586200 | 2 |
| #22586170 | 2 |
| C71×#1546 | 2 |
| #9291 | 71 |