Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
290 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 69 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. C2×#22576088 | C2 | semidirect |
| 3. #31773899 | C2 | semidirect |
| 4. #31773898 | C2 | semidirect |
| 5. #31773763 | C2 | semidirect |
| 6. #31773665 | C2 | semidirect |
| 7. C2×#104×C271 | C2 | semidirect |
| 62. C42×C271 | D4 | semidirect |
| 127. C271 | #2040 | semidirect |
| 131. C2×#104 | D271 | semidirect |
| 190. C42 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774475 | 2 |
| C2×#22576088 | 2 |
| #31773899 | 2 |
| #31773898 | 2 |
| #31773763 | 2 |
| #31773665 | 2 |
| C2×#104×C271 | 2 |
| #2040 | 271 |