Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
282 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 67 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 | #12386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573213 | 2 |
| #22562358 | 2 |
| #22559610 | 2 |
| #22558258 | 2 |
| #22558189 | 2 |
| #22558174 | 2 |
| C67×#2241 | 2 |
| #12386 | 67 |