Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
314 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22560373 | C2 | semidirect |
| 4. #22558318 | C2 | semidirect |
| 5. C67×#1376 | C2 | semidirect |
| 116. #1376 | D67 | semidirect |
| 117. C67 | #13485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561922 | 2 |
| #22561097 | 2 |
| #22560373 | 2 |
| #22558318 | 2 |
| C67×#1376 | 2 |
| #13485 | 67 |