Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
386 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 3. #22577745 | C2 | semidirect |
| 4. #22577745 | C2 | semidirect |
| 5. #22577739 | C2 | semidirect |
| 6. #22577734 | C2 | semidirect |
| 7. #22577445 | C2 | semidirect |
| 8. #22577441 | C2 | semidirect |
| 9. #22577413 | C2 | semidirect |
| 10. C2×#17984013 | C2 | semidirect |
| 126. C137 | #3097 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577974 | 2 |
| #22577886 | 2 |
| #22577745 | 2 |
| #22577739 | 2 |
| #22577734 | 2 |
| #22577445 | 2 |
| #22577441 | 2 |
| #22577413 | 2 |
| C2×#17984013 | 2 |
| #408×C137 | 2 |
| #3097 | 137 |