Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
564 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 564 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×#17984109 | C2 | semidirect |
| 2. C2×#17984107 | C2 | semidirect |
| 3. #22577952 | C2 | semidirect |
| 4. #22577951 | C2 | semidirect |
| 5. #22577798 | C2 | semidirect |
| 6. #22577797 | C2 | semidirect |
| 7. #22577794 | C2 | semidirect |
| 8. #22577791 | C2 | semidirect |
| 9. #22577790 | C2 | semidirect |
| 10. #97×D137 | C2 | semidirect |
| 11. #496×C137 | C2 | semidirect |
| 64. C8×D137 | D4 | semidirect |
| 133. C137 | #3150 | semidirect |
| 144. #496 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984109 | 2 |
| C2×#17984107 | 2 |
| #22577952 | 2 |
| #22577951 | 2 |
| #22577798 | 2 |
| #22577797 | 2 |
| #22577794 | 2 |
| #22577791 | 2 |
| #22577790 | 2 |
| #97×D137 | 2 |
| #496×C137 | 2 |
| #3150 | 137 |