Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
372 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 133 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. #22577773 | C2 | semidirect |
| 3. #22577765 | C2 | semidirect |
| 4. #22577760 | C2 | semidirect |
| 5. #22577755 | C2 | semidirect |
| 6. #22577411 | C2 | semidirect |
| 9. C2×#17984011 | C2 | semidirect |
| 10. #22577359 | C2 | semidirect |
| 11. #544×C137 | C2 | semidirect |
| 127. C137 | #3137 | semidirect |
| 129. #544 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577979 | 2 |
| #22577773 | 2 |
| #22577765 | 2 |
| #22577760 | 2 |
| #22577755 | 2 |
| #22577411 | 2 |
| #22577402 | 2 |
| #22577397 | 2 |
| C2×#17984011 | 2 |
| #22577359 | 2 |
| #544×C137 | 2 |
| #3137 | 137 |