Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
330 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 330 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. #22558317 | C2 | semidirect |
| 4. #22558291 | C2 | semidirect |
| 5. C67×#1845 | C2 | semidirect |
| 119. #1845 | D67 | semidirect |
| 122. C67 | #13484 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561919 | 2 |
| #22561097 | 2 |
| #22558317 | 2 |
| #22558291 | 2 |
| C67×#1845 | 2 |
| #13484 | 67 |