Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
272 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 101 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. C22×C271⋊C16 | C2 | semidirect |
| 3. #31773697 | C2 | direct (N × H) |
| 4. C2×#107×C271 | C2 | semidirect |
| 8. C2×D2168 | C4 | semidirect |
| 11. C2×C271⋊C16 | C22 | semidirect |
| 15. #107×C271 | C22 | semidirect |
| 23. D2168 | C2×C4 | semidirect |
| 62. C2×C271 | #357 | semidirect |
| 67. C271 | C2×#357 | semidirect |
| 71. C2×#107 | D271 | semidirect |
| 83. #107 | C2×D271 | semidirect |
| 131. C2 | #31773697 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D2168 | 2 |
| C22×C271⋊C16 | 2 |
| #31773697 | 2 |
| C2×#107×C271 | 2 |
| C2×#357 | 271 |