Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
228 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 107 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. #11745286 | C2 | semidirect |
| 5. #11745286 | C2 | semidirect |
| 6. #11745259 | C2 | semidirect |
| 7. #11745258 | C2 | semidirect |
| 8. C4⋊C4×D29 | C2 | semidirect |
| 9. #11745251 | C2 | semidirect |
| 10. #11745250 | C2 | semidirect |
| 11. #11745249 | C2 | semidirect |
| 43. C22⋊D29 | Q8 | semidirect |
| 85. C2×C4⋊C4 | D29 | semidirect |
| 86. C29 | #554 | 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 |
| C4×C22⋊D29 | 2 |
| #11745286 | 2 |
| #11745259 | 2 |
| #11745258 | 2 |
| C4⋊C4×D29 | 2 |
| #11745251 | 2 |
| #11745250 | 2 |
| #11745249 | 2 |
| #554 | 29 |