Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
444 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 2. #22587057 | C2 | semidirect |
| 5. #22586204 | C2 | semidirect |
| 6. #22586204 | C2 | semidirect |
| 7. C71×#2381 | C2 | semidirect |
| 10. #17986351 | C4 | semidirect |
| 11. #17986347 | C4 | semidirect |
| 152. #2381 | D71 | semidirect |
| 158. C71 | #9430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598736 | 2 |
| #22587057 | 2 |
| #22586886 | 2 |
| #22586204 | 2 |
| C71×#2381 | 2 |
| #9430 | 71 |