Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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. #31774663 | C2 | semidirect |
| 3. #31773914 | C2 | semidirect |
| 4. #31773870 | C2 | semidirect |
| 5. #31773658 | C2 | semidirect |
| 6. #31773656 | C2 | semidirect |
| 7. #421×C271 | C2 | semidirect |
| 13. #22576158 | C4 | semidirect |
| 14. #22576156 | C4 | semidirect |
| 15. #22576149 | C4 | semidirect |
| 16. #22576147 | C4 | semidirect |
| 38. #16864638 | D4 | semidirect |
| 61. M16×C271 | D4 | semidirect |
| 125. C271 | #1884 | semidirect |
| 130. #421 | D271 | semidirect |
| 176. M16 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774663 | 2 |
| #31774443 | 2 |
| #31773914 | 2 |
| #31773870 | 2 |
| #31773658 | 2 |
| #31773656 | 2 |
| #421×C271 | 2 |
| #1884 | 271 |