Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
684 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 161 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 |
|---|---|---|
| 2. #22588195 | C2 | semidirect |
| 4. #22586223 | C2 | semidirect |
| 5. C71×#1296 | C2 | semidirect |
| 15. #17985742 | C4 | semidirect |
| 35. C4⋊(C71⋊C8) | C2×C4 | semidirect |
| 42. C4⋊C8×C71 | C2×C4 | semidirect |
| 147. #1296 | D71 | semidirect |
| 148. C71 | #8231 | semidirect |
| 184. C4⋊C8 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590902 | 2 |
| #22588195 | 2 |
| C2×#17985742 | 2 |
| #22586223 | 2 |
| C71×#1296 | 2 |
| #8231 | 71 |