Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
388 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 20. #16863212 | C4 | semidirect |
| 158. C67 | #12941 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569077 | 2 |
| #22561995 | 2 |
| C2×#16863212 | 2 |
| #22560992 | 2 |
| #22558305 | 2 |
| #22558297 | 2 |
| C2×#358×C67 | 2 |
| #12941 | 67 |