Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
142 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 57 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. #31774302 | C2 | semidirect |
| 2. #31773724 | C2 | semidirect |
| 3. C4⋊(C271⋊C16) | C2 | semidirect |
| 22. D8×C271 | Q8 | semidirect |
| 55. C271 | #2226 | semidirect |
| 75. D8 | Dic542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774302 | 2 |
| #31773724 | 2 |
| C4⋊(C271⋊C16) | 2 |
| #31773698 | 2 |
| C4×D8×C271 | 2 |
| #2226 | 271 |