Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
182 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 63 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. #31773975 | C2 | semidirect |
| 3. #31773962 | C2 | semidirect |
| 4. #31773649 | C2 | semidirect |
| 5. #31773626 | C2 | semidirect |
| 6. #31773619 | C2 | semidirect |
| 7. D4⋊C8×C271 | C2 | semidirect |
| 44. D1084 | M16 | semidirect |
| 52. C271⋊C8 | D8 | semidirect |
| 83. C271 | #1581 | semidirect |
| 90. D4⋊C8 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#16864639 | 2 |
| #31773975 | 2 |
| #31773962 | 2 |
| #31773649 | 2 |
| #31773626 | 2 |
| #31773619 | 2 |
| D4⋊C8×C271 | 2 |
| #1581 | 271 |