Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
160 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 49 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. #22558414 | C2 | semidirect |
| 4. #22558403 | C2 | semidirect |
| 5. #22558401 | C2 | semidirect |
| 7. C67×#1426 | C2 | semidirect |
| 83. #1426 | D67 | semidirect |
| 87. C67 | #13718 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562318 | 2 |
| #22562002 | 2 |
| #22558414 | 2 |
| #22558403 | 2 |
| #22558401 | 2 |
| #22558348 | 2 |
| C67×#1426 | 2 |
| #13718 | 67 |