Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
428 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×C4×Dic542 | C2 | semidirect |
| 2. #31774213 | C2 | semidirect |
| 3. #31774179 | C2 | semidirect |
| 4. #31774094 | C2 | semidirect |
| 5. #31774035 | C2 | semidirect |
| 6. C4×#16864642 | C2 | semidirect |
| 7. #31773950 | C2 | semidirect |
| 66. Dic542 | #41 | semidirect |
| 83. C2×C4×C271 | SD16 | semidirect |
| 111. C271 | #3103 | semidirect |
| 194. C2×C4 | #16864642 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic542 | 2 |
| #31774213 | 2 |
| #31774179 | 2 |
| #31774094 | 2 |
| #31774035 | 2 |
| C4×#16864642 | 2 |
| #31773950 | 2 |
| #532×C271 | 2 |
| #3103 | 271 |