Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
260 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 85 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. C2×#22576099 | C2 | semidirect |
| 3. C22⋊(C271⋊C16) | C2 | semidirect |
| 4. (C2×D271)⋊C16 | C2 | semidirect |
| 5. C22⋊C16×C271 | C2 | semidirect |
| 14. C2×C271⋊C16 | C22 | semidirect |
| 16. C2×C16×C271 | C22 | semidirect |
| 63. C22×C271 | M32 | semidirect |
| 71. C2×D271 | M32 | semidirect |
| 83. C271 | #2112 | semidirect |
| 89. C22⋊C16 | D271 | semidirect |
| 100. C2×C16 | C2×D271 | semidirect |
| 154. C22 | #22576099 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D271 | 2 |
| C2×#22576099 | 2 |
| C22⋊(C271⋊C16) | 2 |
| (C2×D271)⋊C16 | 2 |
| C22⋊C16×C271 | 2 |
| #2112 | 271 |