Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1182 conjugacy classes of subgroups; only the 371 normal subgroups are shown.
This group has 1182 conjugacy classes of subgroups — too many to draw. Only its 371 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 |
|---|---|---|
| 8. #17985867 | C4 | semidirect |
| 50. C42×C71 | C4⋊C4 | semidirect |
| 95. C71 | #14678 | semidirect |
| 140. C42 | Dic71⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985867 | 2 |
| #22586603 | 2 |
| #22586599 | 2 |
| C2×#384×C71 | 2 |
| #14678 | 71 |