Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
798 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 159 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. #22599464 | C2 | semidirect |
| 2. #22599268 | C2 | semidirect |
| 3. #22599076 | C2 | semidirect |
| 4. #22598794 | C2 | semidirect |
| 5. #22588001 | C2 | semidirect |
| 6. #22587973 | C2 | semidirect |
| 7. #22587966 | C2 | semidirect |
| 8. #22587945 | C2 | semidirect |
| 9. #22587926 | C2 | semidirect |
| 10. #22586638 | C2 | semidirect |
| 11. C71×#1721 | C2 | semidirect |
| 190. #1721 | D71 | semidirect |
| 197. C71 | #19721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599464 | 2 |
| #22599268 | 2 |
| #22599076 | 2 |
| #22598794 | 2 |
| #22588001 | 2 |
| #22587973 | 2 |
| #22587966 | 2 |
| #22587945 | 2 |
| #22587926 | 2 |
| #22586638 | 2 |
| C71×#1721 | 2 |
| #19721 | 71 |