Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
1088 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 202 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 |
|---|---|---|
| 3. C2×(C2×#10587739)⋊C4 | C2 | semidirect |
| 8. C23×#10587739 | C4 | semidirect |
| 13. C2×C22⋊#10587739 | C4 | semidirect |
| 17. C2×C22⋊Dic137 | C4 | semidirect |
| 18. C2×#14555487 | C4 | semidirect |
| 21. C2×C22⋊C4×C137 | C4 | semidirect |
| 34. C22×#10587739 | C2×C4 | semidirect |
| 47. C22×Dic137 | C2×C4 | semidirect |
| 55. C22×C4×C137 | C2×C4 | semidirect |
| 67. C2×#10587739 | C22⋊C4 | semidirect |
| 108. C22×C137 | #95 | semidirect |
| 121. C2×D137 | #95 | semidirect |
| 150. C137 | C22⋊#95 | semidirect |
| 171. C2×C22⋊C4 | #10587739 | semidirect |
| 203. C22×C4 | C2×#10587739 | semidirect |
| 281. C22 | (C2×#10587739)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#10587739 | 2 |
| C22×C22⋊#10587739 | 2 |
| C2×(C2×#10587739)⋊C4 | 2 |
| C2×C22⋊C4×D137 | 2 |
| C22⋊#95 | 137 |