Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
230 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 230 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. C2×#22576103 | C2 | semidirect |
| 2. C2×#22576101 | C2 | semidirect |
| 3. #31774133 | C2 | semidirect |
| 4. #31773701 | C2 | semidirect |
| 5. #31773698 | C2 | semidirect |
| 6. C22⋊(C271⋊C16) | C2 | semidirect |
| 7. C2×#135×C271 | C2 | semidirect |
| 39. Q16×C271 | D4 | semidirect |
| 42. D8×C271 | D4 | semidirect |
| 89. C271 | #2186 | semidirect |
| 91. C2×#135 | D271 | semidirect |
| 123. Q16 | C22⋊D271 | semidirect |
| 128. D8 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576103 | 2 |
| C2×#22576101 | 2 |
| #31774133 | 2 |
| #31773701 | 2 |
| #31773698 | 2 |
| C22⋊(C271⋊C16) | 2 |
| C2×#135×C271 | 2 |
| #2186 | 271 |