Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
564 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 167 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 |
|---|---|---|
| 127. C67 | #8054 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568838 | 2 |
| C2×#16863446 | 2 |
| #22558097 | 2 |
| #22558096 | 2 |
| C67×#1298 | 2 |
| #8054 | 67 |