Finite Group DatabasebetaFinite Group DatabasebetaOrder 29248.
190 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 75 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×C4⋊Dic457 | C2 | semidirect |
| 4. C2×C4×Dic457 | C2 | semidirect |
| 5. #28410459 | C2 | semidirect |
| 6. #28410459 | C2 | semidirect |
| 19. C22⋊C4×C457 | C4 | semidirect |
| 74. C457 | #388 | semidirect |
| 93. C22⋊C4 | Dic457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊Dic457 | 2 |
| C2×C22⋊Dic457 | 2 |
| C2×C4×Dic457 | 2 |
| #28410459 | 2 |
| C2×C22⋊C4×C457 | 2 |
| #388 | 457 |