Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
366 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 147 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 |
|---|---|---|
| 9. #17986401 | C4 | semidirect |
| 111. C71 | #13277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986401 | 2 |
| C2×C4⋊(C71⋊C16) | 2 |
| #22586431 | 2 |
| C4×#107×C71 | 2 |
| #13277 | 71 |