Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
852 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 181 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. C23×Dic542 | C2 | semidirect |
| 2. C2×#22576148 | C2 | semidirect |
| 4. #31773810 | C2 | semidirect |
| 5. #31773803 | C2 | semidirect |
| 6. #31773774 | C2 | semidirect |
| 7. C4×C22⋊C4×C271 | C2 | semidirect |
| 31. C2×Dic542 | D4 | semidirect |
| 81. C22×C271 | #124 | semidirect |
| 101. C271 | #2436 | semidirect |
| 109. C4×C22⋊C4 | D271 | semidirect |
| 187. C22 | #22576148 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic542 | 2 |
| C2×#22576148 | 2 |
| C2×#22576134 | 2 |
| #31773810 | 2 |
| #31773803 | 2 |
| #31773774 | 2 |
| C4×C22⋊C4×C271 | 2 |
| #2436 | 271 |