Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
280 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D29 |
| commutator, socle, cosocle | C22×C29 | C24 |
| Fitting | C4×D4×C29 | C2 |
| prime radical | C2×D4×C29 | C22 |
| hypercenter | C4×D4 | D29 |
| hypocenter | C29 | D4×Q8 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Dic58 | C2 | semidirect |
| 4. #11745286 | C2 | semidirect |
| 5. #11745250 | C2 | semidirect |
| 6. #11745240 | C2 | semidirect |
| 7. #11745231 | C2 | semidirect |
| 8. C4×Dic58 | C2 | semidirect |
| 27. D4×C29 | Q8 | semidirect |
| 39. Dic58 | D4 | direct (N × H) |
| 42. C22×C29 | C2×Q8 | semidirect |
| 47. C4×C29 | C2×Q8 | semidirect |
| 64. C29 | D4×Q8 | semidirect |
| 86. D4 | Dic58 | direct (N × H) |
| 98. C22 | C2×Dic58 | semidirect |
| 105. C4 | C2×Dic58 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic58 | 2 |
| C4×D4×C29 | 2 |
| D4×Dic29 | 2 |
| #11745286 | 2 |
| #11745250 | 2 |
| #11745240 | 2 |
| #11745231 | 2 |
| C4×Dic58 | 2 |
| D4×Q8 | 29 |