Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
210 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 47 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. #31774710 | C2 | semidirect |
| 2. #31774335 | C2 | semidirect |
| 3. C2×#22576103 | C2 | semidirect |
| 4. #31774168 | C2 | semidirect |
| 5. #31773703 | C2 | semidirect |
| 6. #31773682 | C2 | semidirect |
| 7. #362×C271 | C2 | semidirect |
| 90. C271 | #2193 | semidirect |
| 96. #362 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774710 | 2 |
| #31774335 | 2 |
| C2×#22576103 | 2 |
| #31774168 | 2 |
| #31773703 | 2 |
| #31773682 | 2 |
| #362×C271 | 2 |
| #2193 | 271 |