Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
414 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 2. C2×#22576119 | C2 | semidirect |
| 3. #31774239 | C2 | semidirect |
| 4. #31774222 | C2 | semidirect |
| 5. #31773939 | C2 | semidirect |
| 6. #31773899 | C2 | semidirect |
| 7. #407×C271 | C2 | semidirect |
| 20. #22576094 | C22 | semidirect |
| 21. #22576092 | C22 | semidirect |
| 22. #22576085 | C22 | semidirect |
| 23. #22576082 | C22 | semidirect |
| 94. C271 | #3093 | semidirect |
| 102. #407 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774408 | 2 |
| C2×#22576119 | 2 |
| #31774239 | 2 |
| #31774222 | 2 |
| #31773939 | 2 |
| #31773899 | 2 |
| #407×C271 | 2 |
| #3093 | 271 |