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 |
|---|---|---|
| 2. #31774201 | C2 | semidirect |
| 3. #31774194 | C2 | semidirect |
| 4. #31773937 | C2 | semidirect |
| 5. #31773921 | C2 | semidirect |
| 7. C2×#125×C271 | C2 | semidirect |
| 90. C271 | #3080 | semidirect |
| 92. C2×#125 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#16864654 | 2 |
| #31774201 | 2 |
| #31774194 | 2 |
| #31773937 | 2 |
| #31773921 | 2 |
| #31773896 | 2 |
| C2×#125×C271 | 2 |
| #3080 | 271 |