Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
272 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 109 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×C271⋊C16 | C2 | semidirect |
| 2. C2×#22576094 | C2 | semidirect |
| 3. #31773698 | C2 | direct (N × H) |
| 7. C2×C271⋊C16 | C22 | semidirect |
| 9. #22576094 | C22 | semidirect |
| 13. C2×D8×C271 | C4 | semidirect |
| 28. D8×C271 | C2×C4 | semidirect |
| 63. C2×C271 | #357 | semidirect |
| 67. C271 | C2×#357 | semidirect |
| 76. C2×D8 | Dic271 | semidirect |
| 93. D8 | C2×Dic271 | semidirect |
| 131. C2 | #31773698 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C271⋊C16 | 2 |
| C2×#22576094 | 2 |
| #31773698 | 2 |
| C22×D8×C271 | 2 |
| C2×#357 | 271 |