Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
852 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 197 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×#22576149 | C2 | semidirect |
| 3. #31773808 | C2 | semidirect |
| 4. #31773804 | C2 | semidirect |
| 5. #31773776 | C2 | semidirect |
| 6. C4×C22⋊Dic271 | C2 | semidirect |
| 7. C23×Q8×C271 | C2 | semidirect |
| 43. C2×Q8×C271 | D4 | semidirect |
| 81. C22×C271 | #124 | semidirect |
| 101. C271 | #2436 | semidirect |
| 103. C23×Q8 | D271 | semidirect |
| 134. C2×Q8 | C22⋊D271 | semidirect |
| 187. C22 | #22576149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576149 | 2 |
| C2×#22576134 | 2 |
| #31773808 | 2 |
| #31773804 | 2 |
| #31773776 | 2 |
| C4×C22⋊Dic271 | 2 |
| C23×Q8×C271 | 2 |
| #2436 | 271 |