Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
588 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22577419 | C2 | semidirect |
| 3. #22577409 | C2 | semidirect |
| 4. #22577377 | C2 | semidirect |
| 5. #413×C137 | C2 | semidirect |
| 9. C2×#14555510 | C4 | semidirect |
| 11. C22×D548 | C4 | semidirect |
| 15. #17984047 | C22 | semidirect |
| 20. C2×M16×C137 | C22 | semidirect |
| 114. C137 | #1795 | semidirect |
| 119. #413 | D137 | semidirect |
| 131. C2×M16 | C2×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984134 | 2 |
| #22577419 | 2 |
| #22577409 | 2 |
| #22577377 | 2 |
| #413×C137 | 2 |
| #1795 | 137 |