Finite Group DatabasebetaFinite Group DatabasebetaOrder 35968.
320 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 49 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. #31824051 | C2 | semidirect |
| 2. #31823616 | C2 | semidirect |
| 3. #31823599 | C2 | semidirect |
| 4. #31823372 | C2 | semidirect |
| 5. #31823201 | C2 | semidirect |
| 6. #31823198 | C2 | semidirect |
| 7. #323×C281 | C2 | semidirect |
| 28. C2×Dic562 | D4 | semidirect |
| 32. C2×D1124 | D4 | semidirect |
| 43. C4⋊Dic281 | D4 | semidirect |
| 44. C4⋊Dic281 | D4 | semidirect |
| 135. C281 | #1600 | semidirect |
| 143. #323 | D281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31824051 | 2 |
| #31823616 | 2 |
| #31823599 | 2 |
| #31823372 | 2 |
| #31823201 | 2 |
| #31823198 | 2 |
| #323×C281 | 2 |
| #1600 | 281 |