Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 125 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. Q8×Dic542 | C2 | semidirect |
| 3. #31774243 | C2 | semidirect |
| 4. #31774242 | C2 | semidirect |
| 5. #31774188 | C2 | semidirect |
| 6. #31774185 | C2 | semidirect |
| 7. #31774095 | C2 | semidirect |
| 8. #31774021 | C2 | semidirect |
| 9. SD16×Dic271 | C2 | semidirect |
| 10. C4×#16864641 | C2 | semidirect |
| 11. #460×C271 | C2 | semidirect |
| 77. Dic542 | SD16 | semidirect |
| 92. Q8×C271 | #41 | semidirect |
| 125. C271 | #3362 | semidirect |
| 134. #460 | D271 | semidirect |
| 206. Q8 | #16864653 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic542 | 2 |
| #31774567 | 2 |
| #31774243 | 2 |
| #31774242 | 2 |
| #31774188 | 2 |
| #31774185 | 2 |
| #31774095 | 2 |
| #31774021 | 2 |
| SD16×Dic271 | 2 |
| C4×#16864641 | 2 |
| #460×C271 | 2 |
| #3362 | 271 |