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. #22578369 | C2 | semidirect |
| 4. #22578286 | C2 | semidirect |
| 9. C2×#14555519 | C4 | semidirect |
| 11. C22×#11764047 | C4 | semidirect |
| 18. #17984006 | C4 | semidirect |
| 19. #17984005 | C4 | semidirect |
| 20. #100×C137 | C4 | semidirect |
| 77. C137 | #1757 | semidirect |
| 95. #100 | #10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984175 | 2 |
| #22578383 | 2 |
| #22578369 | 2 |
| #22578286 | 2 |
| #22577384 | 2 |
| #1757 | 137 |