Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
384 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22558972 | C2 | semidirect |
| 4. #22558065 | C2 | semidirect |
| 5. C4×#106×C67 | C2 | semidirect |
| 7. #16863526 | C4 | semidirect |
| 8. C8×Dic134 | C4 | semidirect |
| 9. #16863475 | C4 | semidirect |
| 11. C8×D268 | C4 | semidirect |
| 154. C4×#106 | D67 | semidirect |
| 158. C67 | #8694 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569184 | 2 |
| #22558972 | 2 |
| #22558732 | 2 |
| #22558065 | 2 |
| C4×#106×C67 | 2 |
| #8694 | 67 |