Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
434 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 129 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. C4×#16864654 | C2 | semidirect |
| 2. #31774218 | C2 | semidirect |
| 3. #31774189 | C2 | semidirect |
| 4. #31774184 | C2 | semidirect |
| 5. #31774094 | C2 | semidirect |
| 6. #31774089 | C2 | semidirect |
| 7. #31774040 | C2 | semidirect |
| 8. C4×#16864642 | C2 | semidirect |
| 9. C4×#16864639 | C2 | semidirect |
| 10. #31773950 | C2 | semidirect |
| 11. #532×C271 | C2 | semidirect |
| 85. Dic542 | #41 | semidirect |
| 87. D1084 | #41 | semidirect |
| 144. C271 | #3106 | semidirect |
| 146. #532 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#16864654 | 2 |
| #31774218 | 2 |
| #31774189 | 2 |
| #31774184 | 2 |
| #31774094 | 2 |
| #31774089 | 2 |
| #31774040 | 2 |
| C4×#16864642 | 2 |
| C4×#16864639 | 2 |
| #31773950 | 2 |
| #532×C271 | 2 |
| #3106 | 271 |