Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
214 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 7. #17985775 | C4 | semidirect |
| 8. #17985752 | C4 | semidirect |
| 90. C71 | #7222 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590143 | 2 |
| #22587103 | 2 |
| C71×#1834 | 2 |
| #7222 | 71 |