Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
798 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 179 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. #22598898 | C2 | semidirect |
| 2. #22598897 | C2 | semidirect |
| 3. #22598849 | C2 | semidirect |
| 5. #22587974 | C2 | semidirect |
| 6. #22587973 | C2 | semidirect |
| 7. #22587966 | C2 | semidirect |
| 8. #22587961 | C2 | semidirect |
| 9. #22587960 | C2 | semidirect |
| 10. #322×D71 | C2 | semidirect |
| 11. C71×#1715 | C2 | semidirect |
| 106. C8×D71 | SD16 | semidirect |
| 188. #1715 | D71 | semidirect |
| 192. C71 | #19608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598898 | 2 |
| #22598897 | 2 |
| #22598849 | 2 |
| #22598767 | 2 |
| #22587974 | 2 |
| #22587973 | 2 |
| #22587966 | 2 |
| #22587961 | 2 |
| #22587960 | 2 |
| #322×D71 | 2 |
| C71×#1715 | 2 |
| #19608 | 71 |