Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
370 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 370 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. #31774622 | C2 | semidirect |
| 3. #31774246 | C2 | semidirect |
| 4. #31774180 | C2 | semidirect |
| 5. #31774179 | C2 | semidirect |
| 8. C8×Dic542 | C2 | semidirect |
| 11. #487×C271 | C2 | semidirect |
| 78. Dic542 | SD16 | semidirect |
| 118. C271 | #3359 | semidirect |
| 123. #487 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774622 | 2 |
| #31774562 | 2 |
| #31774246 | 2 |
| #31774180 | 2 |
| #31774179 | 2 |
| #31774101 | 2 |
| #31774099 | 2 |
| C8×Dic542 | 2 |
| C4×#16864643 | 2 |
| #31773982 | 2 |
| #487×C271 | 2 |
| #3359 | 271 |