Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 384 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×#22576151 | C2 | semidirect |
| 3. #31774206 | C2 | semidirect |
| 4. #31774202 | C2 | semidirect |
| 5. #31774199 | C2 | semidirect |
| 6. #31774195 | C2 | semidirect |
| 7. #31773939 | C2 | semidirect |
| 8. #31773937 | C2 | semidirect |
| 9. #31773920 | C2 | semidirect |
| 135. C271 | #3080 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576151 | 2 |
| #41×Dic271 | 2 |
| #31774206 | 2 |
| #31774202 | 2 |
| #31774199 | 2 |
| #31774195 | 2 |
| #31773939 | 2 |
| #31773937 | 2 |
| #31773920 | 2 |
| #31773898 | 2 |
| #417×C271 | 2 |
| #3080 | 271 |