Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
362 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 362 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. #31774206 | C2 | semidirect |
| 4. #31774202 | C2 | semidirect |
| 5. #31774190 | C2 | semidirect |
| 6. #31774180 | C2 | semidirect |
| 65. C2×Q8×C271 | Q8 | semidirect |
| 116. C271 | #3082 | semidirect |
| 161. C2×Q8 | Dic542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774528 | 2 |
| #31774375 | 2 |
| #31774206 | 2 |
| #31774202 | 2 |
| #31774190 | 2 |
| #31774180 | 2 |
| #31773937 | 2 |
| #31773935 | 2 |
| #31773923 | 2 |
| #31773906 | 2 |
| C2×#103×C271 | 2 |
| #3082 | 271 |