Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
484 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 221 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. #31774380 | C2 | semidirect |
| 2. #31774009 | C2 | semidirect |
| 3. #31774004 | C2 | semidirect |
| 4. SD16×Dic271 | C2 | semidirect |
| 5. C2×#22576092 | C2 | semidirect |
| 6. #31773898 | C2 | semidirect |
| 7. #31773852 | C2 | semidirect |
| 24. #135×C271 | C4 | semidirect |
| 42. #41×C271 | C2×C4 | semidirect |
| 48. Q16×C271 | C2×C4 | semidirect |
| 49. SD16×C271 | C2×C4 | semidirect |
| 50. D8×C271 | C2×C4 | semidirect |
| 51. C2×C8×C271 | C2×C4 | semidirect |
| 90. C271 | #2952 | semidirect |
| 101. #135 | Dic271 | semidirect |
| 121. #41 | C2×Dic271 | semidirect |
| 129. Q16 | C2×Dic271 | semidirect |
| 130. SD16 | C2×Dic271 | semidirect |
| 131. D8 | C2×Dic271 | semidirect |
| 134. C2×C8 | C2×Dic271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774380 | 2 |
| #31774009 | 2 |
| #31774004 | 2 |
| SD16×Dic271 | 2 |
| C2×#22576092 | 2 |
| #31773898 | 2 |
| #31773852 | 2 |
| C2×#135×C271 | 2 |
| #2952 | 271 |