Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
330 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D29 |
| commutator, socle, cosocle | C22×C29 | C24 |
| Frattini | C22 | C23×D29 |
| Fitting | C23×C4×C29 | C2 |
| hypercenter | C23×C4 | D29 |
| hypocenter | C29 | #525 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C2×C4 ◁ C23×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C4×C29 | C2 | semidirect |
| 2. C2×#90805 | C2 | semidirect |
| 3. #11745315 | C2 | semidirect |
| 4. #11745292 | C2 | semidirect |
| 5. #11745291 | C2 | semidirect |
| 6. C4×C22⋊D29 | C2 | semidirect |
| 7. #11745288 | C2 | semidirect |
| 8. #11745286 | C2 | semidirect |
| 18. C2×D116 | C22 | semidirect |
| 19. C2×C4×D29 | C22 | semidirect |
| 20. C2×Dic58 | C22 | semidirect |
| 23. #90781 | C22 | semidirect |
| 24. C4⋊Dic29 | C22 | semidirect |
| 25. #90779 | C22 | semidirect |
| 26. C4×Dic29 | C22 | semidirect |
| 35. C2×C4×C29 | D4 | semidirect |
| 51. C22×C29 | #41 | semidirect |
| 67. C23×C4 | D29 | semidirect |
| 74. C29 | #525 | semidirect |
| 108. C2×C4 | C22⋊D29 | semidirect |
| 118. C22 | #90805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×C29 | 2 |
| C2×#90805 | 2 |
| #11745315 | 2 |
| #11745292 | 2 |
| #11745291 | 2 |
| C4×C22⋊D29 | 2 |
| #11745288 | 2 |
| #11745286 | 2 |
| #525 | 29 |