Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 1. C2×#17984114 | C2 | semidirect |
| 2. #22577953 | C2 | semidirect |
| 3. #22577790 | C2 | semidirect |
| 4. #22577779 | C2 | semidirect |
| 5. #22577775 | C2 | semidirect |
| 6. C4×#14555494 | C2 | semidirect |
| 7. C2×#127×C137 | C2 | semidirect |
| 10. C2×#14555498 | C22 | semidirect |
| 11. C2×#14555495 | C22 | semidirect |
| 13. #17984088 | C22 | semidirect |
| 14. #17984085 | C22 | semidirect |
| 15. #17984076 | C22 | semidirect |
| 18. #17983999 | C22 | semidirect |
| 19. C4×#11764040 | C22 | semidirect |
| 34. #14555494 | D4 | semidirect |
| 57. #11764040 | C2×D4 | semidirect |
| 82. C4×C137 | AGL(1,ℤ/8) | semidirect |
| 90. C137 | #3151 | semidirect |
| 94. C2×#127 | D137 | semidirect |
| 174. C4 | #17984114 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984114 | 2 |
| #22577953 | 2 |
| #22577790 | 2 |
| #22577779 | 2 |
| #22577775 | 2 |
| C4×#14555494 | 2 |
| C2×#127×C137 | 2 |
| #3151 | 137 |