Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 149 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×#22576190 | C2 | semidirect |
| 2. C2×#22576185 | C2 | semidirect |
| 3. C2×#22576148 | C2 | semidirect |
| 4. #31774289 | C2 | semidirect |
| 5. #31774284 | C2 | semidirect |
| 6. #31774279 | C2 | semidirect |
| 7. C4×#16864638 | C2 | semidirect |
| 8. #532×C271 | C2 | semidirect |
| 13. C2×#16864644 | C22 | semidirect |
| 14. C2×#16864642 | C22 | semidirect |
| 22. #22576071 | C22 | semidirect |
| 23. C4×C271⋊C8 | C22 | semidirect |
| 25. C4⋊Q8×C271 | C22 | semidirect |
| 26. #127×C271 | C22 | semidirect |
| 27. #124×C271 | C22 | semidirect |
| 43. #16864638 | D4 | semidirect |
| 106. C271 | #3153 | semidirect |
| 110. #532 | D271 | semidirect |
| 126. C4⋊Q8 | C2×D271 | semidirect |
| 127. #127 | C2×D271 | semidirect |
| 131. #124 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576190 | 2 |
| C2×#22576185 | 2 |
| C2×#22576148 | 2 |
| #31774289 | 2 |
| #31774284 | 2 |
| #31774279 | 2 |
| C4×#16864638 | 2 |
| #532×C271 | 2 |
| #3153 | 271 |