Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
306 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 29. C4×C8×C71 | C8 | semidirect |
| 92. C71 | #8800 | semidirect |
| 117. C4×C8 | C71⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22586185 | 2 |
| #22586173 | 2 |
| #22586171 | 2 |
| C4×#97×C71 | 2 |
| #8800 | 71 |