Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
316 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 2. #22561813 | C2 | semidirect |
| 4. #22561000 | C2 | semidirect |
| 5. #22558321 | C2 | semidirect |
| 6. #22558320 | C2 | semidirect |
| 21. #361×C67 | C4 | semidirect |
| 137. C67 | #13158 | semidirect |
| 149. #361 | Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863209 | 2 |
| #22561813 | 2 |
| #22561120 | 2 |
| #22561000 | 2 |
| #22558321 | 2 |
| #22558320 | 2 |
| C2×#361×C67 | 2 |
| #13158 | 67 |