Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
148 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 45 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×D4336 | C2 | semidirect |
| 2. #31774313 | C2 | semidirect |
| 3. #31774168 | C2 | semidirect |
| 4. #31773709 | C2 | semidirect |
| 5. #368×C271 | C2 | semidirect |
| 54. C271 | #2221 | semidirect |
| 59. #368 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4336 | 2 |
| #31774313 | 2 |
| #31774168 | 2 |
| #31773709 | 2 |
| #368×C271 | 2 |
| #2221 | 271 |