Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
442 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 10. #17986404 | C4 | semidirect |
| 11. #17986350 | C4 | semidirect |
| 172. C71 | #9298 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599493 | 2 |
| #22591086 | 2 |
| #22589320 | 2 |
| #22587026 | 2 |
| #22586903 | 2 |
| #22586168 | 2 |
| C71×#1286 | 2 |
| #9298 | 71 |