Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
350 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22578127 | C2 | semidirect |
| 2. #22578114 | C2 | semidirect |
| 3. #22577759 | C2 | semidirect |
| 4. #22577712 | C2 | semidirect |
| 5. #22577690 | C2 | semidirect |
| 7. #22577605 | C2 | semidirect |
| 8. C8×Dic274 | C2 | semidirect |
| 9. #22577488 | C2 | semidirect |
| 11. #487×C137 | C2 | semidirect |
| 120. C137 | #3360 | semidirect |
| 125. #487 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578127 | 2 |
| #22578114 | 2 |
| #22577759 | 2 |
| #22577712 | 2 |
| #22577690 | 2 |
| #22577621 | 2 |
| #22577605 | 2 |
| C8×Dic274 | 2 |
| #22577488 | 2 |
| C4×D1096 | 2 |
| #487×C137 | 2 |
| #3360 | 137 |