Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
492 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 145 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. #31774447 | C2 | semidirect |
| 2. #31774210 | C2 | semidirect |
| 3. #31774177 | C2 | semidirect |
| 4. #31774092 | C2 | semidirect |
| 5. #31774031 | C2 | semidirect |
| 6. C4×#16864639 | C2 | semidirect |
| 7. #31773950 | C2 | semidirect |
| 8. C2×C4×D4×C271 | C2 | semidirect |
| 11. #22576160 | C22 | semidirect |
| 12. #22576157 | C22 | semidirect |
| 17. C4×D1084 | C22 | semidirect |
| 18. #22576093 | C22 | semidirect |
| 19. C4⋊(C271⋊C8) | C22 | semidirect |
| 21. #22576080 | C22 | semidirect |
| 23. C4×C271⋊C8 | C22 | semidirect |
| 81. D4×C271 | #41 | semidirect |
| 88. C2×C4×C271 | D8 | semidirect |
| 120. C271 | #3100 | semidirect |
| 123. C2×C4×D4 | D271 | semidirect |
| 199. D4 | #16864654 | semidirect |
| 208. C2×C4 | #16864639 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774447 | 2 |
| #31774210 | 2 |
| #31774177 | 2 |
| #31774092 | 2 |
| #31774031 | 2 |
| C4×#16864639 | 2 |
| #31773950 | 2 |
| C2×C4×D4×C271 | 2 |
| #3100 | 271 |