Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
716 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 209 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. #22577880 | C2 | semidirect |
| 3. #22577377 | C2 | semidirect |
| 4. #22577376 | C2 | semidirect |
| 5. #22577375 | C2 | semidirect |
| 6. #410×C137 | C2 | semidirect |
| 9. C2×#14555510 | C4 | semidirect |
| 11. C2×#14555509 | C4 | semidirect |
| 13. C22×Dic274 | C4 | semidirect |
| 15. C2×Q8×D137 | C4 | semidirect |
| 113. C137 | #2884 | semidirect |
| 120. #410 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984135 | 2 |
| #22577880 | 2 |
| #22577377 | 2 |
| #22577376 | 2 |
| #22577375 | 2 |
| #410×C137 | 2 |
| #2884 | 137 |