Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
438 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 438 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. C2×#22576122 | C2 | semidirect |
| 3. C2×#22576080 | C2 | semidirect |
| 4. C2×#22576080 | C2 | semidirect |
| 5. #31773798 | C2 | semidirect |
| 6. #31773651 | C2 | semidirect |
| 7. #340×C271 | C2 | semidirect |
| 13. C2×D2168 | C4 | semidirect |
| 37. C2×D1084 | C2×C4 | semidirect |
| 59. C2×C8×C271 | C2×C4 | semidirect |
| 85. D1084 | C22⋊C4 | semidirect |
| 91. C2×Dic271 | D8 | semidirect |
| 146. C271 | #1879 | semidirect |
| 153. #340 | D271 | semidirect |
| 201. C2×C8 | C4×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D2168 | 2 |
| C2×#22576122 | 2 |
| C2×#22576080 | 2 |
| #31773798 | 2 |
| #31773651 | 2 |
| #340×C271 | 2 |
| #1879 | 271 |