Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
560 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 197 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. #22577293 | C2 | semidirect |
| 4. #22577269 | C2 | semidirect |
| 5. #22577265 | C2 | semidirect |
| 6. C4×C4⋊Dic137 | C2 | semidirect |
| 7. #22577250 | C2 | semidirect |
| 8. C4×C4⋊C4×C137 | C2 | semidirect |
| 11. C4×D548 | C4 | semidirect |
| 97. C137 | #2357 | semidirect |
| 105. C4×C4⋊C4 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D548 | 2 |
| #22577305 | 2 |
| #22577293 | 2 |
| #22577269 | 2 |
| #22577265 | 2 |
| C4×C4⋊Dic137 | 2 |
| #22577250 | 2 |
| C4×C4⋊C4×C137 | 2 |
| #2357 | 137 |