Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. #125×D137 | C2 | semidirect |
| 3. #22577770 | C2 | semidirect |
| 4. #22577766 | C2 | semidirect |
| 5. #22577760 | C2 | semidirect |
| 6. #22577758 | C2 | semidirect |
| 7. #22577757 | C2 | semidirect |
| 8. #22577403 | C2 | semidirect |
| 9. #22577401 | C2 | semidirect |
| 10. C4×#14555493 | C2 | semidirect |
| 11. #488×C137 | C2 | semidirect |
| 114. C137 | #3142 | semidirect |
| 123. #488 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577952 | 2 |
| #125×D137 | 2 |
| #22577770 | 2 |
| #22577766 | 2 |
| #22577760 | 2 |
| #22577758 | 2 |
| #22577757 | 2 |
| #22577403 | 2 |
| #22577401 | 2 |
| C4×#14555493 | 2 |
| #488×C137 | 2 |
| #3142 | 137 |