Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
780 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 780 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 |
|---|---|---|
| 3. #22591980 | C2 | semidirect |
| 4. #22586861 | C2 | semidirect |
| 6. #22586225 | C2 | semidirect |
| 7. C71×#1784 | C2 | semidirect |
| 227. #1784 | D71 | semidirect |
| 231. C71 | #10330 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599147 | 2 |
| #22591994 | 2 |
| #22591980 | 2 |
| #22586861 | 2 |
| #22586857 | 2 |
| #22586225 | 2 |
| C71×#1784 | 2 |
| #10330 | 71 |