Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
214 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 99 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⋊C4×C29 | C2 | semidirect |
| 4. #11745288 | C2 | semidirect |
| 5. #11745286 | C2 | semidirect |
| 6. #11745260 | C2 | semidirect |
| 7. #11745259 | C2 | semidirect |
| 8. #11745254 | C2 | semidirect |
| 9. #11745252 | C2 | semidirect |
| 10. #11745251 | C2 | semidirect |
| 11. #11745249 | C2 | semidirect |
| 83. C2×C4⋊C4 | D29 | semidirect |
| 84. C29 | #552 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊C4×C29 | 2 |
| #11745291 | 2 |
| C4×C22⋊D29 | 2 |
| #11745288 | 2 |
| #11745286 | 2 |
| #11745260 | 2 |
| #11745259 | 2 |
| #11745254 | 2 |
| #11745252 | 2 |
| #11745251 | 2 |
| #11745249 | 2 |
| #552 | 29 |