Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
590 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 151 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. #499×D71 | C2 | semidirect |
| 3. #22590585 | C2 | semidirect |
| 4. #22590583 | C2 | semidirect |
| 5. #22590582 | C2 | semidirect |
| 6. #22590573 | C2 | semidirect |
| 7. #22590051 | C2 | semidirect |
| 8. #22589933 | C2 | semidirect |
| 9. C71×#2245 | C2 | semidirect |
| 152. #2245 | D71 | semidirect |
| 158. C71 | #33708 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #499×D71 | 2 |
| #22598769 | 2 |
| #22590585 | 2 |
| #22590583 | 2 |
| #22590582 | 2 |
| #22590573 | 2 |
| #22590051 | 2 |
| #22589933 | 2 |
| C71×#2245 | 2 |
| #33708 | 71 |