Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
392 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22558976 | C2 | semidirect |
| 4. #22558103 | C2 | semidirect |
| 19. #329×C67 | C4 | semidirect |
| 20. #329×C67 | C4 | semidirect |
| 21. #329×C67 | C4 | semidirect |
| 143. C67 | #8918 | semidirect |
| 157. #329 | Dic67 | semidirect |
| 158. #329 | Dic67 | semidirect |
| 159. #329 | Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569280 | 2 |
| #22561042 | 2 |
| #22558976 | 2 |
| #22558103 | 2 |
| C67×#1525 | 2 |
| #8918 | 67 |