Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 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×#22576166 | C2 | semidirect |
| 2. #31774471 | C2 | semidirect |
| 4. #31774140 | C2 | semidirect |
| 5. #31774123 | C2 | semidirect |
| 6. #31773935 | C2 | semidirect |
| 7. #31773906 | C2 | semidirect |
| 8. #31773902 | C2 | semidirect |
| 9. C22×SD16×C271 | C2 | semidirect |
| 13. C2×#16864637 | C22 | semidirect |
| 14. C2×C8×D271 | C22 | semidirect |
| 20. #22576136 | C22 | semidirect |
| 25. #22576094 | C22 | semidirect |
| 26. #22576092 | C22 | semidirect |
| 27. #22576084 | C22 | semidirect |
| 68. C2×C8×C271 | D4 | semidirect |
| 120. C271 | #3057 | semidirect |
| 122. C22×SD16 | D271 | semidirect |
| 180. C2×C8 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576166 | 2 |
| #31774471 | 2 |
| #31774464 | 2 |
| #31774140 | 2 |
| #31774123 | 2 |
| #31773935 | 2 |
| #31773906 | 2 |
| #31773902 | 2 |
| C22×SD16×C271 | 2 |
| #3057 | 271 |