Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
460 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 127 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. C2×Q16×D271 | C2 | semidirect |
| 4. #31774156 | C2 | semidirect |
| 5. #31774155 | C2 | semidirect |
| 6. #31774152 | C2 | semidirect |
| 7. #31774137 | C2 | semidirect |
| 8. #31774136 | C2 | semidirect |
| 9. #31773932 | C2 | semidirect |
| 10. #31773904 | C2 | semidirect |
| 11. #470×C271 | C2 | semidirect |
| 133. C271 | #3059 | semidirect |
| 141. #470 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D271 | 2 |
| C2×#22576168 | 2 |
| #31774470 | 2 |
| #31774156 | 2 |
| #31774155 | 2 |
| #31774152 | 2 |
| #31774137 | 2 |
| #31774136 | 2 |
| #31773932 | 2 |
| #31773904 | 2 |
| #470×C271 | 2 |
| #3059 | 271 |