Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
816 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 229 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D29 |
| commutator | C22×C29 | C23×C4 |
| Fitting | C29×#380 | C2 |
| socle, cosocle | C23×C29 | C24 |
| prime radical | C24×D29 | C22 |
| hypercenter | #380 | D29 |
| hypocenter | C29 | #2315 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #14271037 | C2 | semidirect |
| 4. #14271034 | C2 | semidirect |
| 5. #14271023 | C2 | semidirect |
| 6. #14271021 | C2 | semidirect |
| 7. C29×#380 | C2 | semidirect |
| 12. C2×C4⋊C4×C29 | C22 | semidirect |
| 15. C2×#90781 | C4 | semidirect |
| 19. C2×C4⋊Dic29 | C22 | semidirect |
| 20. C2×#90779 | C22 | semidirect |
| 22. C29×#95 | C22 | semidirect |
| 23. #11745179 | C22 | semidirect |
| 24. #11745179 | C22 | semidirect |
| 33. C22×C4×C29 | C2×C4 | semidirect |
| 38. C22×Dic29 | C2×C4 | semidirect |
| 48. #90781 | C2×C4 | semidirect |
| 49. #90781 | C2×C4 | semidirect |
| 64. C22×D29 | C4⋊C4 | semidirect |
| 111. #380 | D29 | semidirect |
| 125. C2×C4⋊C4 | C2×D29 | semidirect |
| 135. #95 | C2×D29 | semidirect |
| 136. C29 | #2315 | semidirect |
| 152. C22×C4 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90781 | 2 |
| C2×C22⋊C4×D29 | 2 |
| #14271037 | 2 |
| #14271034 | 2 |
| #14271023 | 2 |
| #14271021 | 2 |
| C29×#380 | 2 |
| #2315 | 29 |