Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
284 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 89 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. C4×C4⋊Dic137 | C2 | semidirect |
| 3. #22577138 | C2 | semidirect |
| 4. #431×C137 | C2 | semidirect |
| 6. #17984088 | C4 | semidirect |
| 7. #17984085 | C4 | semidirect |
| 12. C4×D548 | C4 | semidirect |
| 89. C137 | #1502 | semidirect |
| 92. #431 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577953 | 2 |
| C4×C4⋊Dic137 | 2 |
| #22577138 | 2 |
| #431×C137 | 2 |
| #1502 | 137 |