Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
598 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#22576074 | C2 | semidirect |
| 3. #31773753 | C2 | semidirect |
| 4. #31773663 | C2 | semidirect |
| 5. C22×C22⋊C4×C271 | C2 | semidirect |
| 6. C22×C22⋊D271 | C4 | semidirect |
| 12. C2×C22⋊Dic271 | C4 | semidirect |
| 21. C23×D271 | C2×C4 | semidirect |
| 30. C22×Dic271 | C2×C4 | semidirect |
| 31. C22×Dic271 | C2×C4 | semidirect |
| 52. C22⋊C4×C271 | D4 | semidirect |
| 108. C22×C271 | #99 | semidirect |
| 130. C271 | #1898 | semidirect |
| 133. C22×C22⋊C4 | D271 | semidirect |
| 183. C22⋊C4 | C22⋊D271 | semidirect |
| 242. C22 | #22576074 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576129 | 2 |
| C2×#22576074 | 2 |
| #31773753 | 2 |
| #31773663 | 2 |
| C22×C22⋊C4×C271 | 2 |
| #1898 | 271 |