Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
302 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 89 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. #31773937 | C2 | semidirect |
| 4. #31773766 | C2 | semidirect |
| 5. #31773665 | C2 | semidirect |
| 6. #31773658 | C2 | semidirect |
| 20. #22576087 | C4 | semidirect |
| 30. #16864638 | C2×C4 | semidirect |
| 43. C4×Dic271 | C2×C4 | semidirect |
| 71. Q8×C271 | C4⋊C4 | semidirect |
| 75. D4×C271 | C4⋊C4 | semidirect |
| 112. C271 | #1859 | semidirect |
| 175. Q8 | Dic271⋊C4 | semidirect |
| 179. D4 | Dic271⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774380 | 2 |
| #31773937 | 2 |
| C2×#22576087 | 2 |
| #31773766 | 2 |
| #31773665 | 2 |
| #31773658 | 2 |
| #417×C271 | 2 |
| #1859 | 271 |