Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
444 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 91 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. C22×#16864642 | C2 | semidirect |
| 2. C2×#22576140 | C2 | semidirect |
| 4. C2×#22576085 | C2 | semidirect |
| 5. C2×(C2×D271)⋊C8 | C2 | semidirect |
| 6. #31773659 | C2 | semidirect |
| 7. C2×#102×C271 | C2 | semidirect |
| 35. C2×Dic542 | D4 | semidirect |
| 51. C2×C271⋊C8 | D4 | semidirect |
| 70. C4⋊C4×C271 | D4 | semidirect |
| 77. C22×D271 | SD16 | semidirect |
| 157. C271 | #2000 | semidirect |
| 163. C2×#102 | D271 | semidirect |
| 226. C4⋊C4 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864642 | 2 |
| C2×#22576140 | 2 |
| C2×#22576131 | 2 |
| C2×#22576085 | 2 |
| C2×(C2×D271)⋊C8 | 2 |
| #31773659 | 2 |
| C2×#102×C271 | 2 |
| #2000 | 271 |