Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
264 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 97 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×C4⋊(C271⋊C8) | C2 | semidirect |
| 3. #31773629 | C2 | semidirect |
| 4. #31773626 | C2 | semidirect |
| 5. #431×C271 | C2 | semidirect |
| 24. #16864654 | C8 | semidirect |
| 53. Dic542 | C2×C8 | semidirect |
| 55. D1084 | C2×C8 | semidirect |
| 101. C271 | #1477 | semidirect |
| 104. #431 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#16864654 | 2 |
| C2×C4⋊(C271⋊C8) | 2 |
| #31773629 | 2 |
| #31773626 | 2 |
| #431×C271 | 2 |
| #1477 | 271 |