Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
296 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 15. #17985816 | C4 | semidirect |
| 132. C71 | #13157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985816 | 2 |
| C2×#17985814 | 2 |
| #22589944 | 2 |
| #22589253 | 2 |
| #22589128 | 2 |
| #22586453 | 2 |
| C71×#1388 | 2 |
| #13157 | 71 |