Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
228 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 9. #22576095 | C4 | direct (N × H) |
| 48. C4×C271 | #108 | semidirect |
| 55. C271 | C4×#108 | semidirect |
| 104. C4 | #22576095 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576095 | 2 |
| C4×#16864638 | 2 |
| C2×C4×C271⋊C8 | 2 |
| #31773661 | 2 |
| C4×M16×C271 | 2 |
| C4×#108 | 271 |