Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
446 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 111 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. #17986294 | C4 | semidirect |
| 11. #17986284 | C4 | semidirect |
| 186. C71 | #9178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598145 | 2 |
| #22591305 | 2 |
| #22586905 | 2 |
| #22586840 | 2 |
| #22586242 | 2 |
| #22586199 | 2 |
| C71×#1479 | 2 |
| #9178 | 71 |