Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
180 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 1. C8×Dic542 | C2 | semidirect |
| 4. #31773648 | C2 | semidirect |
| 5. #31773629 | C2 | semidirect |
| 7. C82×C271 | C2 | semidirect |
| 26. #16864643 | C8 | direct (N × H) |
| 43. Dic542 | C2×C8 | semidirect |
| 59. C8×C271 | C2×C8 | semidirect |
| 60. C8×C271 | SD16 | semidirect |
| 77. C271 | C8×SD16 | semidirect |
| 85. C82 | D271 | semidirect |
| 137. C8 | C8×D271 | semidirect |
| 138. C8 | #16864643 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Dic542 | 2 |
| C4×#16864643 | 2 |
| C8×D1084 | 2 |
| #31773648 | 2 |
| #31773629 | 2 |
| #31773626 | 2 |
| C82×C271 | 2 |
| C8×SD16 | 271 |