Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
334 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. #31773907 | C2 | semidirect |
| 5. #31773802 | C2 | semidirect |
| 6. #31773658 | C2 | semidirect |
| 7. #343×C271 | C2 | semidirect |
| 11. #22576193 | C4 | semidirect |
| 37. C2×Dic542 | C2×C4 | semidirect |
| 61. M16×C271 | C2×C4 | semidirect |
| 124. C271 | #1882 | semidirect |
| 131. #343 | D271 | semidirect |
| 177. M16 | C4×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576193 | 2 |
| #31774378 | 2 |
| C2×#22576086 | 2 |
| #31773907 | 2 |
| #31773802 | 2 |
| #31773658 | 2 |
| #343×C271 | 2 |
| #1882 | 271 |