Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
356 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 356 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 |
|---|---|---|
| 21. #17985745 | C4 | semidirect |
| 22. #17985745 | C4 | semidirect |
| 23. #17985745 | C4 | semidirect |
| 24. #17985745 | C4 | semidirect |
| 157. C71 | #8936 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597442 | 2 |
| #22587131 | 2 |
| #22587005 | 2 |
| #22586173 | 2 |
| C71×#1994 | 2 |
| #8936 | 71 |