Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
728 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 728 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 |
|---|---|---|
| 2. #22599058 | C2 | semidirect |
| 3. #22598734 | C2 | semidirect |
| 4. #22598721 | C2 | semidirect |
| 5. #22587993 | C2 | semidirect |
| 6. #22587986 | C2 | semidirect |
| 7. #22587979 | C2 | semidirect |
| 8. #22587952 | C2 | semidirect |
| 9. C71×#1455 | C2 | semidirect |
| 167. #1455 | D71 | semidirect |
| 168. C71 | #19754 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599078 | 2 |
| #22599058 | 2 |
| #22598734 | 2 |
| #22598721 | 2 |
| #22587993 | 2 |
| #22587986 | 2 |
| #22587979 | 2 |
| #22587952 | 2 |
| C71×#1455 | 2 |
| #19754 | 71 |