Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
934 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 934 conjugacy classes of subgroups — too many to draw. Only its 183 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. #22587382 | C2 | semidirect |
| 5. #22586852 | C2 | semidirect |
| 6. #22586684 | C2 | semidirect |
| 7. C71×#3502 | C2 | semidirect |
| 183. #3502 | D71 | semidirect |
| 190. C71 | #18188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598435 | 2 |
| #22591623 | 2 |
| #22587382 | 2 |
| #22587280 | 2 |
| #22586852 | 2 |
| #22586684 | 2 |
| C71×#3502 | 2 |
| #18188 | 71 |