Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
532 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 137 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×#17984117 | C2 | semidirect |
| 3. C2×Q16×D137 | C2 | semidirect |
| 4. #22577973 | C2 | semidirect |
| 5. #22577798 | C2 | semidirect |
| 6. #22577794 | C2 | semidirect |
| 7. #22577786 | C2 | semidirect |
| 8. #22577783 | C2 | semidirect |
| 9. #22577781 | C2 | semidirect |
| 10. #22577357 | C2 | semidirect |
| 11. #495×C137 | C2 | semidirect |
| 121. C137 | #3156 | semidirect |
| 130. #495 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984117 | 2 |
| C2×#17984107 | 2 |
| C2×Q16×D137 | 2 |
| #22577973 | 2 |
| #22577798 | 2 |
| #22577794 | 2 |
| #22577786 | 2 |
| #22577783 | 2 |
| #22577781 | 2 |
| #22577357 | 2 |
| #495×C137 | 2 |
| #3156 | 137 |