Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22577743 | C2 | semidirect |
| 4. #22577742 | C2 | semidirect |
| 5. #22577737 | C2 | semidirect |
| 6. #22577732 | C2 | semidirect |
| 7. #22577443 | C2 | semidirect |
| 8. #22577441 | C2 | semidirect |
| 9. #22577412 | C2 | semidirect |
| 11. C2×#103×C137 | C2 | semidirect |
| 126. C137 | #3097 | semidirect |
| 137. C2×#103 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577977 | 2 |
| #22577884 | 2 |
| #22577743 | 2 |
| #22577742 | 2 |
| #22577737 | 2 |
| #22577732 | 2 |
| #22577443 | 2 |
| #22577441 | 2 |
| #22577412 | 2 |
| #22577369 | 2 |
| C2×#103×C137 | 2 |
| #3097 | 137 |