Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
436 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 436 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×#22576160 | C2 | semidirect |
| 3. #31774257 | C2 | direct (N × H) |
| 4. C2×#22576085 | C2 | semidirect |
| 6. C2×#97×C271 | C2 | semidirect |
| 11. #22576160 | C22 | semidirect |
| 18. #22576085 | C22 | semidirect |
| 22. #97×C271 | C22 | semidirect |
| 82. C2×C271 | #489 | semidirect |
| 87. C271 | C2×#489 | semidirect |
| 94. C2×#97 | D271 | semidirect |
| 110. #97 | C2×D271 | semidirect |
| 171. C2 | #31774257 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576160 | 2 |
| C2×#22576148 | 2 |
| #31774257 | 2 |
| C2×#22576085 | 2 |
| C2×#22576082 | 2 |
| C2×#97×C271 | 2 |
| C2×#489 | 271 |