Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
272 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 13. #17985826 | C4 | semidirect |
| 14. #17985824 | C4 | semidirect |
| 129. C71 | #13118 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590129 | 2 |
| #22589078 | 2 |
| #22586450 | 2 |
| #22586445 | 2 |
| #22586440 | 2 |
| #22586420 | 2 |
| C71×#1773 | 2 |
| #13118 | 71 |