Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
216 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 47 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. C4⋊Q8×C71 | C8 | semidirect |
| 76. C71 | #7355 | semidirect |
| 86. C4⋊Q8 | C71⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22586286 | 2 |
| C71×#1956 | 2 |
| #7355 | 71 |