Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
434 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 121 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. #31774448 | C2 | semidirect |
| 2. C4×#16864655 | C2 | semidirect |
| 3. #31774224 | C2 | semidirect |
| 4. #31774184 | C2 | semidirect |
| 5. #31774097 | C2 | semidirect |
| 6. #31774093 | C2 | semidirect |
| 7. #31774045 | C2 | semidirect |
| 8. #31773982 | C2 | semidirect |
| 9. #31773979 | C2 | semidirect |
| 10. #31773949 | C2 | semidirect |
| 11. #477×C271 | C2 | semidirect |
| 93. D1084 | #41 | semidirect |
| 109. Q8×C271 | #41 | semidirect |
| 144. C271 | #3106 | semidirect |
| 149. #477 | D271 | semidirect |
| 233. Q8 | #16864655 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774448 | 2 |
| C4×#16864655 | 2 |
| #31774224 | 2 |
| #31774184 | 2 |
| #31774097 | 2 |
| #31774093 | 2 |
| #31774045 | 2 |
| #31773982 | 2 |
| #31773979 | 2 |
| #31773949 | 2 |
| #477×C271 | 2 |
| #3106 | 271 |