Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
164 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 49 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. C2×#22576104 | C2 | semidirect |
| 2. C2×C16×D271 | C2 | semidirect |
| 3. #31774139 | C2 | semidirect |
| 5. #31773724 | C2 | semidirect |
| 6. #31773702 | C2 | semidirect |
| 7. #357×C271 | C2 | semidirect |
| 33. C271⋊C16 | D4 | semidirect |
| 63. C2×D271 | SD32 | semidirect |
| 75. C271 | #2217 | semidirect |
| 83. #357 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576104 | 2 |
| C2×C16×D271 | 2 |
| #31774139 | 2 |
| #31774130 | 2 |
| #31773724 | 2 |
| #31773702 | 2 |
| #357×C271 | 2 |
| #2217 | 271 |