Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
420 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 123 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. #31774562 | C2 | semidirect |
| 3. #31774226 | C2 | semidirect |
| 4. #31774179 | C2 | semidirect |
| 5. #31774129 | C2 | semidirect |
| 6. #31774099 | C2 | semidirect |
| 7. #31774037 | C2 | semidirect |
| 8. C4×#16864643 | C2 | semidirect |
| 9. C8×D1084 | C2 | semidirect |
| 10. #103×D271 | C2 | semidirect |
| 11. #487×C271 | C2 | semidirect |
| 81. Dic542 | #41 | semidirect |
| 85. D1084 | SD16 | semidirect |
| 128. C271 | #3298 | semidirect |
| 132. #487 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774562 | 2 |
| #31774550 | 2 |
| #31774226 | 2 |
| #31774179 | 2 |
| #31774129 | 2 |
| #31774099 | 2 |
| #31774037 | 2 |
| C4×#16864643 | 2 |
| C8×D1084 | 2 |
| #103×D271 | 2 |
| #487×C271 | 2 |
| #3298 | 271 |