Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
368 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 129 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. #31774301 | C2 | semidirect |
| 3. #31774275 | C2 | semidirect |
| 4. #31774246 | C2 | semidirect |
| 8. C4×Dic1084 | C2 | semidirect |
| 9. C4×#16864644 | C2 | semidirect |
| 11. C4×Q16×C271 | C2 | semidirect |
| 83. C4×D271 | Q16 | semidirect |
| 114. C271 | #3170 | semidirect |
| 125. C4×Q16 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774451 | 2 |
| #31774301 | 2 |
| #31774275 | 2 |
| #31774246 | 2 |
| #31774139 | 2 |
| #31774137 | 2 |
| #31774135 | 2 |
| C4×Dic1084 | 2 |
| C4×#16864644 | 2 |
| C4×C8×D271 | 2 |
| C4×Q16×C271 | 2 |
| #3170 | 271 |