Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
492 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 492 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. #22560426 | C2 | semidirect |
| 4. #22558335 | C2 | semidirect |
| 19. #355×C67 | C4 | semidirect |
| 47. #101×C67 | C2×C4 | semidirect |
| 145. C67 | #12972 | semidirect |
| 157. #355 | Dic67 | semidirect |
| 183. #101 | C2×Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22563321 | 2 |
| #22560613 | 2 |
| #22560426 | 2 |
| #22558335 | 2 |
| C2×#355×C67 | 2 |
| #12972 | 67 |