Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
380 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 71 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. #28409830 | C2 | semidirect |
| 2. C2×#20300314 | C2 | semidirect |
| 3. #28409049 | C2 | semidirect |
| 4. #28409037 | C2 | semidirect |
| 5. #28409005 | C2 | semidirect |
| 6. #28408802 | C2 | semidirect |
| 7. #535×C227 | C2 | semidirect |
| 35. C2×Dic454 | D4 | semidirect |
| 36. C2×D908 | D4 | semidirect |
| 48. #16813868 | D4 | semidirect |
| 50. C2×C227⋊C8 | D4 | semidirect |
| 142. C227 | #2008 | semidirect |
| 146. #535 | D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28409830 | 2 |
| C2×#20300314 | 2 |
| #28409049 | 2 |
| #28409037 | 2 |
| #28409005 | 2 |
| #28408802 | 2 |
| #535×C227 | 2 |
| #2008 | 227 |