Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 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 |
|---|---|---|
| 3. #22577811 | C2 | semidirect |
| 4. #22577810 | C2 | semidirect |
| 5. #22577805 | C2 | semidirect |
| 6. #22577802 | C2 | semidirect |
| 7. #22577802 | C2 | semidirect |
| 11. #499×C137 | C2 | semidirect |
| 43. #14555493 | Q8 | semidirect |
| 44. #14555493 | Q8 | semidirect |
| 99. C137 | #3166 | semidirect |
| 108. #499 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577959 | 2 |
| #125×D137 | 2 |
| #22577811 | 2 |
| #22577810 | 2 |
| #22577805 | 2 |
| #22577802 | 2 |
| #22577444 | 2 |
| #22577442 | 2 |
| C4×#14555493 | 2 |
| #499×C137 | 2 |
| #3166 | 137 |