Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
852 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 173 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. C22×Q8×D271 | C2 | semidirect |
| 2. C2×#22576147 | C2 | semidirect |
| 4. #31773809 | C2 | semidirect |
| 5. #31773804 | C2 | semidirect |
| 6. #31773803 | C2 | semidirect |
| 7. #31773773 | C2 | semidirect |
| 8. C4×(C2×D271)⋊C4 | C2 | semidirect |
| 9. C2×#124×C271 | C2 | semidirect |
| 39. C2×Dic542 | D4 | semidirect |
| 61. C2×Q8×C271 | D4 | semidirect |
| 122. C2×D271 | #124 | semidirect |
| 137. C271 | #2436 | semidirect |
| 141. C2×#124 | D271 | semidirect |
| 182. C2×Q8 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D271 | 2 |
| C2×#22576147 | 2 |
| C2×#22576131 | 2 |
| #31773809 | 2 |
| #31773804 | 2 |
| #31773803 | 2 |
| #31773773 | 2 |
| C4×(C2×D271)⋊C4 | 2 |
| C2×#124×C271 | 2 |
| #2436 | 271 |