Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 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. #22577956 | C2 | semidirect |
| 3. #22577770 | C2 | semidirect |
| 4. #22577766 | C2 | semidirect |
| 5. #22577764 | C2 | semidirect |
| 6. #22577761 | C2 | semidirect |
| 7. #22577400 | C2 | semidirect |
| 8. #22577399 | C2 | semidirect |
| 9. #22577397 | C2 | semidirect |
| 10. C2×#17983998 | C2 | semidirect |
| 11. #416×C137 | C2 | semidirect |
| 125. C137 | #3135 | semidirect |
| 136. #416 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577956 | 2 |
| #22577949 | 2 |
| #22577770 | 2 |
| #22577766 | 2 |
| #22577764 | 2 |
| #22577761 | 2 |
| #22577400 | 2 |
| #22577399 | 2 |
| #22577397 | 2 |
| C2×#17983998 | 2 |
| #416×C137 | 2 |
| #3135 | 137 |