Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 458 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 |
|---|---|---|
| 3. #31774375 | C2 | semidirect |
| 4. #31774121 | C2 | semidirect |
| 5. #31774105 | C2 | semidirect |
| 6. #31773923 | C2 | semidirect |
| 7. #31773906 | C2 | semidirect |
| 9. C22×Q16×C271 | C2 | semidirect |
| 111. C271 | #3044 | semidirect |
| 114. C22×Q16 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576191 | 2 |
| #31774471 | 2 |
| #31774375 | 2 |
| #31774121 | 2 |
| #31774105 | 2 |
| #31773923 | 2 |
| #31773906 | 2 |
| #31773894 | 2 |
| C22×Q16×C271 | 2 |
| #3044 | 271 |