Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
778 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 253 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. C2×#17984095 | C2 | semidirect |
| 3. #22577407 | C2 | semidirect |
| 4. #22577402 | C2 | semidirect |
| 5. #22577397 | C2 | semidirect |
| 6. C2×#17984008 | C2 | semidirect |
| 7. #520×C137 | C2 | semidirect |
| 9. #17984134 | C4 | semidirect |
| 15. C2×#14555494 | C22 | semidirect |
| 16. C22×#11764040 | C22 | semidirect |
| 17. #17984011 | C22 | semidirect |
| 18. #17984011 | C22 | semidirect |
| 19. #17984008 | C22 | semidirect |
| 20. #17984008 | C22 | semidirect |
| 21. #17984008 | C22 | semidirect |
| 25. #117×C137 | C22 | semidirect |
| 26. C2×C4⋊C4×C137 | C22 | semidirect |
| 30. #14555510 | C2×C4 | semidirect |
| 34. C2×D548 | C2×C4 | semidirect |
| 97. C137 | #2897 | semidirect |
| 101. #520 | D137 | semidirect |
| 118. #117 | C2×D137 | semidirect |
| 119. C2×C4⋊C4 | 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 |
| C2×#17984095 | 2 |
| #22577407 | 2 |
| #22577402 | 2 |
| #22577397 | 2 |
| C2×#17984008 | 2 |
| #520×C137 | 2 |
| #2897 | 137 |