Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 131 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×#20300307 | C2 | semidirect |
| 2. #28409580 | C2 | semidirect |
| 3. C4×#16813883 | C2 | semidirect |
| 4. #28409253 | C2 | semidirect |
| 5. #28409245 | C2 | semidirect |
| 6. #28409243 | C2 | semidirect |
| 7. #28409237 | C2 | semidirect |
| 8. #28409229 | C2 | semidirect |
| 9. C4⋊C8×D227 | C2 | semidirect |
| 10. #28409025 | C2 | semidirect |
| 11. #459×C227 | C2 | semidirect |
| 47. #16813883 | D4 | semidirect |
| 135. C4×C227 | #135 | semidirect |
| 150. C227 | #3035 | semidirect |
| 160. #459 | D227 | semidirect |
| 292. C4 | #20300307 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20300307 | 2 |
| #28409580 | 2 |
| C4×#16813883 | 2 |
| #28409253 | 2 |
| #28409245 | 2 |
| #28409243 | 2 |
| #28409237 | 2 |
| #28409229 | 2 |
| C4⋊C8×D227 | 2 |
| #28409025 | 2 |
| #459×C227 | 2 |
| #3035 | 227 |