Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
380 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 80 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. #22578345 | C2 | semidirect |
| 3. #22578281 | C2 | semidirect |
| 13. C2×#14555489 | C4 | semidirect |
| 14. C2×C22⋊Dic137 | C4 | semidirect |
| 16. C2×C4×Dic137 | C4 | semidirect |
| 17. C23×C4×C137 | C4 | semidirect |
| 61. C2×Dic137 | C4⋊C4 | semidirect |
| 68. C23×C137 | C4⋊C4 | semidirect |
| 97. C4×C137 | #99 | semidirect |
| 109. C137 | #1799 | semidirect |
| 117. C23×C4 | #10587739 | semidirect |
| 164. C23 | C4⋊#10587739 | semidirect |
| 210. C4 | #17984146 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984146 | 2 |
| #22578345 | 2 |
| #22578281 | 2 |
| C2×C4×C22⋊D137 | 2 |
| #1799 | 137 |