Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
704 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 145 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×#22576191 | C2 | semidirect |
| 3. #31774471 | C2 | semidirect |
| 4. #31774078 | C2 | semidirect |
| 5. #31774073 | C2 | semidirect |
| 6. #31773914 | C2 | semidirect |
| 7. #31773913 | C2 | semidirect |
| 8. #31773879 | C2 | semidirect |
| 9. C2×#137×C271 | C2 | semidirect |
| 23. #22576191 | C22 | semidirect |
| 26. C2×#16864638 | C22 | semidirect |
| 27. #22576158 | C22 | semidirect |
| 28. #22576149 | C22 | semidirect |
| 31. #22576119 | C22 | semidirect |
| 32. #22576087 | C22 | semidirect |
| 33. #22576086 | C22 | semidirect |
| 34. #22576078 | C22 | semidirect |
| 35. #22576076 | C22 | semidirect |
| 37. C22×Q8×C271 | C22 | semidirect |
| 39. #137×C271 | C22 | semidirect |
| 42. C2×M16×C271 | C22 | semidirect |
| 192. C271 | #3022 | semidirect |
| 196. C2×#137 | D271 | semidirect |
| 216. C22×Q8 | C2×D271 | semidirect |
| 220. #137 | C2×D271 | semidirect |
| 226. C2×M16 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774733 | 2 |
| C2×#22576191 | 2 |
| #31774471 | 2 |
| #31774078 | 2 |
| #31774073 | 2 |
| #31773914 | 2 |
| #31773913 | 2 |
| #31773879 | 2 |
| C2×#137×C271 | 2 |
| #3022 | 271 |