Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
136 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 1. C4⋊(C71⋊C32) | C2 | semidirect |
| 2. #22586414 | C2 | semidirect |
| 70. C71 | #7446 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊(C71⋊C32) | 2 |
| #22586414 | 2 |
| C71×#2249 | 2 |
| #7446 | 71 |