Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
220 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 69 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. #28409430 | C2 | semidirect |
| 3. #28409405 | C2 | semidirect |
| 4. #28409379 | C2 | semidirect |
| 5. #322×C227 | C2 | semidirect |
| 38. C8×C227 | SD16 | semidirect |
| 51. C227 | #1715 | semidirect |
| 57. #322 | D227 | semidirect |
| 90. C8 | #16813873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28409430 | 2 |
| #28409409 | 2 |
| #28409405 | 2 |
| #28409379 | 2 |
| #322×C227 | 2 |
| #1715 | 227 |