Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
380 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 5. #31774180 | C2 | semidirect |
| 6. #31774105 | C2 | semidirect |
| 8. #31774004 | C2 | semidirect |
| 9. #31774001 | C2 | semidirect |
| 127. C271 | #3113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774449 | 2 |
| C2×Q8×Dic271 | 2 |
| #31774228 | 2 |
| #31774225 | 2 |
| #31774180 | 2 |
| #31774105 | 2 |
| #31774053 | 2 |
| #31774004 | 2 |
| #31774001 | 2 |
| #31773951 | 2 |
| #451×C271 | 2 |
| #3113 | 271 |