Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
426 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 426 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. #31774567 | C2 | semidirect |
| 2. D4×Dic542 | C2 | semidirect |
| 3. #31774243 | C2 | semidirect |
| 4. #31774242 | C2 | semidirect |
| 5. #31774178 | C2 | semidirect |
| 6. #31774175 | C2 | semidirect |
| 7. #31774090 | C2 | semidirect |
| 8. #31774021 | C2 | semidirect |
| 9. D8×Dic271 | C2 | semidirect |
| 10. C4×#16864639 | C2 | semidirect |
| 11. #459×C271 | C2 | semidirect |
| 78. Dic542 | D8 | semidirect |
| 99. D4×C271 | #41 | semidirect |
| 131. C271 | #3358 | semidirect |
| 140. #459 | D271 | semidirect |
| 222. D4 | #16864653 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774567 | 2 |
| D4×Dic542 | 2 |
| #31774243 | 2 |
| #31774242 | 2 |
| #31774178 | 2 |
| #31774175 | 2 |
| #31774090 | 2 |
| #31774021 | 2 |
| D8×Dic271 | 2 |
| C4×#16864639 | 2 |
| #459×C271 | 2 |
| #3358 | 271 |