Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
568 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 3. #22587057 | C2 | semidirect |
| 5. #22586852 | C2 | semidirect |
| 6. #22586234 | C2 | semidirect |
| 7. C71×#3165 | C2 | semidirect |
| 186. #3165 | D71 | semidirect |
| 192. C71 | #10102 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599339 | 2 |
| #22594452 | 2 |
| #22587057 | 2 |
| #22586937 | 2 |
| #22586852 | 2 |
| #22586234 | 2 |
| C71×#3165 | 2 |
| #10102 | 71 |