Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
408 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22588560 | C2 | semidirect |
| 5. #22586470 | C2 | semidirect |
| 6. #22586469 | C2 | semidirect |
| 7. C71×#1858 | C2 | semidirect |
| 20. #17985797 | C4 | semidirect |
| 21. #17985795 | C4 | semidirect |
| 192. #1858 | D71 | semidirect |
| 195. C71 | #12974 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597409 | 2 |
| #22590023 | 2 |
| #22588723 | 2 |
| #22588560 | 2 |
| #22586470 | 2 |
| #22586469 | 2 |
| C71×#1858 | 2 |
| #12974 | 71 |