Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
880 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 229 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×#22576117 | C2 | semidirect |
| 3. C2×C4⋊C4×D271 | C2 | semidirect |
| 4. #31773803 | C2 | semidirect |
| 5. #31773802 | C2 | semidirect |
| 6. #31773800 | C2 | semidirect |
| 7. #31773773 | C2 | semidirect |
| 8. #31773755 | C2 | semidirect |
| 9. #390×C271 | C2 | semidirect |
| 12. C2×#16864653 | C4 | semidirect |
| 36. C2×Dic542 | C2×C4 | semidirect |
| 42. C22×Dic271 | C2×C4 | semidirect |
| 61. C2×D4×C271 | C2×C4 | semidirect |
| 88. C4×D271 | C22⋊C4 | semidirect |
| 133. C271 | #2311 | semidirect |
| 141. #390 | D271 | semidirect |
| 177. C2×D4 | C4×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864653 | 2 |
| C2×#22576117 | 2 |
| C2×C4⋊C4×D271 | 2 |
| #31773803 | 2 |
| #31773802 | 2 |
| #31773800 | 2 |
| #31773773 | 2 |
| #31773755 | 2 |
| #390×C271 | 2 |
| #2311 | 271 |