Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
396 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22577751 | C2 | semidirect |
| 3. #22577727 | C2 | semidirect |
| 4. #22577685 | C2 | semidirect |
| 5. #22577634 | C2 | semidirect |
| 6. #22577603 | C2 | semidirect |
| 7. #22577563 | C2 | semidirect |
| 8. C4×#14555500 | C2 | semidirect |
| 9. D4×#11764040 | C2 | semidirect |
| 10. #22577397 | C2 | semidirect |
| 11. #556×C137 | C2 | semidirect |
| 127. C137 | #3304 | semidirect |
| 129. #556 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578074 | 2 |
| #22577751 | 2 |
| #22577727 | 2 |
| #22577685 | 2 |
| #22577634 | 2 |
| #22577603 | 2 |
| #22577563 | 2 |
| C4×#14555500 | 2 |
| D4×#11764040 | 2 |
| #22577397 | 2 |
| #556×C137 | 2 |
| #3304 | 137 |