Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
308 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 2. #31774244 | C2 | semidirect |
| 3. #31774177 | C2 | semidirect |
| 4. #31774103 | C2 | semidirect |
| 5. #31773640 | C2 | semidirect |
| 6. #31773626 | C2 | semidirect |
| 7. D4⋊C8×C271 | C2 | semidirect |
| 11. #22576160 | C22 | semidirect |
| 18. C4⋊(C271⋊C8) | C22 | semidirect |
| 23. C4⋊C8×C271 | C22 | semidirect |
| 24. C4×C8×C271 | C22 | semidirect |
| 75. D4×C271 | SD16 | semidirect |
| 109. C271 | #1639 | semidirect |
| 117. D4⋊C8 | D271 | semidirect |
| 130. C4⋊C8 | C2×D271 | semidirect |
| 134. C4×C8 | C2×D271 | semidirect |
| 180. D4 | #16864643 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D1084 | 2 |
| #31774244 | 2 |
| #31774177 | 2 |
| #31774103 | 2 |
| #31773640 | 2 |
| #31773626 | 2 |
| D4⋊C8×C271 | 2 |
| #1639 | 271 |