Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
336 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 4. C2×#17983998 | C2 | semidirect |
| 5. C2×C8×Dic137 | C2 | semidirect |
| 6. #22577158 | C2 | semidirect |
| 7. #336×C137 | C2 | semidirect |
| 16. #17984000 | C4 | semidirect |
| 17. #17984000 | C4 | semidirect |
| 104. C137 | #1750 | semidirect |
| 112. #336 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984045 | 2 |
| C2×#17984000 | 2 |
| C2×#17983998 | 2 |
| C2×C8×Dic137 | 2 |
| #22577158 | 2 |
| #336×C137 | 2 |
| #1750 | 137 |