Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
292 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 53. C4×C271 | #101 | semidirect |
| 61. C271 | #1966 | semidirect |
| 116. C4 | #22576078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576160 | 2 |
| #31773921 | 2 |
| C2×#22576078 | 2 |
| C4×M16×C271 | 2 |
| #1966 | 271 |