Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
456 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 3. #31774005 | C2 | semidirect |
| 4. #31774004 | C2 | semidirect |
| 5. #31774003 | C2 | semidirect |
| 6. C4×#16864644 | C2 | semidirect |
| 7. #31773989 | C2 | semidirect |
| 11. #441×C271 | C2 | semidirect |
| 15. Q16×D271 | C4 | semidirect |
| 108. C271 | #2950 | semidirect |
| 115. #441 | 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 |
| #31774373 | 2 |
| #31774005 | 2 |
| #31774004 | 2 |
| #31774003 | 2 |
| C4×#16864644 | 2 |
| #31773989 | 2 |
| #31773932 | 2 |
| #31773904 | 2 |
| #31773854 | 2 |
| #441×C271 | 2 |
| #2950 | 271 |