Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
426 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 141 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. #31774569 | C2 | semidirect |
| 2. #31774245 | C2 | semidirect |
| 3. #31774174 | C2 | semidirect |
| 4. #31774092 | C2 | semidirect |
| 5. Q8×C271⋊C8 | C2 | semidirect |
| 6. C4×#16864639 | C2 | semidirect |
| 7. D4×Q8×C271 | C2 | semidirect |
| 55. Q8×C271 | D8 | semidirect |
| 57. D4×C271 | #41 | semidirect |
| 81. C271 | #3358 | semidirect |
| 84. D4×Q8 | D271 | semidirect |
| 129. Q8 | #16864639 | semidirect |
| 135. D4 | #16864655 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774569 | 2 |
| #31774245 | 2 |
| #31774174 | 2 |
| #31774092 | 2 |
| Q8×C271⋊C8 | 2 |
| C4×#16864639 | 2 |
| D4×Q8×C271 | 2 |
| #3358 | 271 |