Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
310 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 19. #17985819 | C4 | semidirect |
| 133. C71 | #13181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590128 | 2 |
| #22590126 | 2 |
| C2×#17985819 | 2 |
| #22588498 | 2 |
| #22588222 | 2 |
| #22586450 | 2 |
| C71×#1387 | 2 |
| #13181 | 71 |