Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
284 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 86 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. #22578367 | C2 | semidirect |
| 4. #22578284 | C2 | semidirect |
| 8. C2×#14555520 | C4 | semidirect |
| 9. C2×#14555519 | C4 | semidirect |
| 12. C2×#14555518 | C4 | semidirect |
| 13. C22×#11764047 | C4 | semidirect |
| 15. #17984149 | C4 | semidirect |
| 16. #17984148 | C4 | semidirect |
| 97. C137 | #1757 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984175 | 2 |
| #22578390 | 2 |
| #22578367 | 2 |
| #22578284 | 2 |
| #22577375 | 2 |
| #1757 | 137 |