Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
444 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 444 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 |
|---|---|---|
| 1. #31774372 | C2 | semidirect |
| 2. #31773902 | C2 | semidirect |
| 3. C2×#22576077 | C2 | semidirect |
| 4. #31773657 | C2 | semidirect |
| 16. #127×C271 | C4 | semidirect |
| 22. C4⋊Dic271 | D4 | semidirect |
| 36. C2×D4×C271 | C2×C4 | semidirect |
| 41. C42×C271 | C2×C4 | semidirect |
| 87. C271 | #1887 | semidirect |
| 99. #127 | Dic271 | semidirect |
| 116. C2×D4 | C2×Dic271 | semidirect |
| 129. C42 | C2×Dic271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774372 | 2 |
| #31773902 | 2 |
| C2×#22576077 | 2 |
| #31773657 | 2 |
| C2×#127×C271 | 2 |
| #1887 | 271 |