Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
568 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 154 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 |
|---|---|---|
| 10. C2×C4×#10587739 | C4 | semidirect |
| 13. (C2×#10587739)⋊C4 | C4 | semidirect |
| 16. #17983995 | C4 | semidirect |
| 17. #17983995 | C4 | semidirect |
| 18. #95×C137 | C4 | semidirect |
| 138. C137 | #1434 | semidirect |
| 157. #95 | #10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#10587739 | 2 |
| C2×(C2×#10587739)⋊C4 | 2 |
| #95×D137 | 2 |
| #1434 | 137 |