Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22578034 | C2 | semidirect |
| 3. #22577770 | C2 | semidirect |
| 4. #22577761 | C2 | semidirect |
| 5. #22577756 | C2 | semidirect |
| 6. #22577752 | C2 | semidirect |
| 7. #22577413 | C2 | semidirect |
| 9. C2×#17984011 | C2 | semidirect |
| 10. #22577361 | C2 | semidirect |
| 127. C137 | #3137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578034 | 2 |
| #22577974 | 2 |
| #22577770 | 2 |
| #22577761 | 2 |
| #22577756 | 2 |
| #22577752 | 2 |
| #22577413 | 2 |
| #22577399 | 2 |
| C2×#17984011 | 2 |
| #22577361 | 2 |
| #417×C137 | 2 |
| #3137 | 137 |