Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
360 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. C2×#22576091 | C2 | semidirect |
| 5. #31773660 | C2 | semidirect |
| 6. #31773659 | C2 | semidirect |
| 7. C2×#106×C271 | C2 | semidirect |
| 18. (C2×D271)⋊C8 | C4 | semidirect |
| 39. C2×C271⋊C8 | C2×C4 | semidirect |
| 51. C2×C8×C271 | C2×C4 | semidirect |
| 105. C2×D271 | #106 | semidirect |
| 123. C271 | #1853 | semidirect |
| 127. C2×#106 | D271 | semidirect |
| 169. C2×C8 | C4×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊C4×D271 | 2 |
| C2×#22576091 | 2 |
| C2×(C2×D271)⋊C8 | 2 |
| #31773754 | 2 |
| #31773660 | 2 |
| #31773659 | 2 |
| C2×#106×C271 | 2 |
| #1853 | 271 |