Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
184 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. C4⋊(C271⋊C16) | C2 | semidirect |
| 4. Dic271⋊C16 | C2 | semidirect |
| 5. C4⋊C16×C271 | C2 | semidirect |
| 37. C4×D271 | C16 | semidirect |
| 53. C4×C271 | C2×C16 | semidirect |
| 58. Dic271 | C2×C16 | semidirect |
| 62. D271 | C4⋊C16 | direct (N × H) |
| 63. C271 | C2×C4⋊C16 | semidirect |
| 69. C4⋊C16 | D271 | direct (N × H) |
| 120. C4 | C16×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C16×D271 | 2 |
| C4×C8×D271 | 2 |
| C4⋊(C271⋊C16) | 2 |
| Dic271⋊C16 | 2 |
| C4⋊C16×C271 | 2 |
| C2×C4⋊C16 | 271 |