Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
468 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 468 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. C2×#22576193 | C2 | semidirect |
| 3. C22×#16864643 | C2 | semidirect |
| 4. C2×#22576166 | C2 | semidirect |
| 5. #31774161 | C2 | direct (N × H) |
| 6. C2×#22576078 | C2 | semidirect |
| 7. C2×#22576076 | C2 | semidirect |
| 8. C2×#108×C271 | C2 | semidirect |
| 13. #22576193 | C22 | semidirect |
| 22. C2×#16864643 | C22 | semidirect |
| 25. #22576166 | C22 | semidirect |
| 29. #22576078 | C22 | semidirect |
| 30. #22576076 | C22 | semidirect |
| 34. #108×C271 | C22 | semidirect |
| 134. C2×C271 | #471 | semidirect |
| 138. C271 | C2×#471 | semidirect |
| 145. C2×#108 | D271 | semidirect |
| 171. #108 | C2×D271 | semidirect |
| 275. C2 | #31774161 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576193 | 2 |
| C2×#22576188 | 2 |
| C22×#16864643 | 2 |
| C2×#22576166 | 2 |
| #31774161 | 2 |
| C2×#22576078 | 2 |
| C2×#22576076 | 2 |
| C2×#108×C271 | 2 |
| C2×#471 | 271 |