Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1290 conjugacy classes of subgroups; only the 327 normal subgroups are shown.
This group has 1290 conjugacy classes of subgroups — too many to draw. Only its 327 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 |
|---|---|---|
| 1. #22586602 | C2 | semidirect |
| 4. #22586572 | C2 | semidirect |
| 15. #399×C71 | C4 | semidirect |
| 135. C71 | #14618 | semidirect |
| 141. #399 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22586602 | 2 |
| #22586589 | 2 |
| #22586577 | 2 |
| #22586572 | 2 |
| C2×#399×C71 | 2 |
| #14618 | 71 |