Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
266 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 61 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×#22576101 | C2 | semidirect |
| 2. #31774133 | C2 | semidirect |
| 3. #31773698 | C2 | semidirect |
| 4. C22⋊(C271⋊C16) | C2 | semidirect |
| 5. C22×D8×C271 | C2 | semidirect |
| 6. C2×D2168 | C22 | semidirect |
| 9. C2×C271⋊C16 | C22 | semidirect |
| 10. #22576094 | C22 | semidirect |
| 31. D8×C271 | D4 | semidirect |
| 60. C22×C271 | D16 | semidirect |
| 75. C271 | #2184 | semidirect |
| 77. C22×D8 | D271 | semidirect |
| 104. D8 | C22⋊D271 | semidirect |
| 139. C22 | #22576101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576101 | 2 |
| #31774133 | 2 |
| #31773698 | 2 |
| C22⋊(C271⋊C16) | 2 |
| C22×D8×C271 | 2 |
| #2184 | 271 |