Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
222 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 81 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. #31773924 | C2 | semidirect |
| 4. C2×#22576070 | C2 | semidirect |
| 5. #31773662 | C2 | semidirect |
| 6. #31773656 | C2 | semidirect |
| 19. #103×C271 | C4 | semidirect |
| 20. #102×C271 | C4 | semidirect |
| 90. C271 | #1938 | semidirect |
| 108. #103 | Dic271 | semidirect |
| 109. #102 | Dic271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31773924 | 2 |
| C2×#22576087 | 2 |
| #31773864 | 2 |
| C2×#22576070 | 2 |
| #31773662 | 2 |
| #31773656 | 2 |
| #416×C271 | 2 |
| #1938 | 271 |