Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 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.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×D116 |
| commutator, cosocle | C4×C29 | C24 |
| Frattini | C4 | C23×D29 |
| Fitting | C29×#131 | C2 |
| socle | C2×C29 | C22×D4 |
| hypercenter | #131 | D29 |
| hypocenter | C29 | #577 |
| LCS | G ▷ C4×C29 ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ #131 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11745365 | C2 | semidirect |
| 2. #11745364 | C2 | semidirect |
| 3. C29×#131 | C2 | semidirect |
| 4. #11745271 | C2 | semidirect |
| 5. #11745270 | C2 | semidirect |
| 6. #11745266 | C2 | semidirect |
| 7. C2×#90773 | C2 | semidirect |
| 14. #90805 | C22 | semidirect |
| 16. C2×Dic58 | C22 | semidirect |
| 17. M16×C29 | C22 | semidirect |
| 18. C2×C8×C29 | C22 | semidirect |
| 19. Dic116 | C22 | semidirect |
| 20. D232 | C22 | semidirect |
| 21. #90773 | C22 | semidirect |
| 22. #90773 | C22 | semidirect |
| 23. #90773 | C22 | semidirect |
| 60. #131 | D29 | semidirect |
| 61. C29 | #577 | semidirect |
| 76. M16 | C2×D29 | semidirect |
| 77. C2×C8 | C2×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11745365 | 2 |
| #11745364 | 2 |
| C29×#131 | 2 |
| #11745271 | 2 |
| #11745270 | 2 |
| #11745266 | 2 |
| C2×#90773 | 2 |
| #577 | 29 |