Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
336 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 113 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. #22577746 | C2 | semidirect |
| 3. #22577740 | C2 | semidirect |
| 4. #22577707 | C2 | semidirect |
| 5. #22577662 | C2 | semidirect |
| 6. C4×Dic548 | C2 | semidirect |
| 8. #22577442 | C2 | semidirect |
| 9. #499×C137 | C2 | semidirect |
| 96. C137 | #3352 | semidirect |
| 99. #499 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578091 | 2 |
| #22577746 | 2 |
| #22577740 | 2 |
| #22577707 | 2 |
| #22577662 | 2 |
| C4×Dic548 | 2 |
| #22577482 | 2 |
| #22577442 | 2 |
| #499×C137 | 2 |
| #3352 | 137 |