Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
360 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 209 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C23×D29 |
| commutator, socle | C2×C29 | C23×C8 |
| Fitting | C29×#504 | C2 |
| prime radical | #41×D29 | C4 |
| cosocle | C8×C29 | C24 |
| hypercenter | #504 | D29 |
| hypocenter | C29 | #3407 |
| LCS | G ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C8 ◁ #504 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14271581 | C2 | semidirect |
| 3. #14271580 | C2 | semidirect |
| 4. #14271579 | C2 | semidirect |
| 5. C2×#11745146 | C2 | semidirect |
| 6. M32×D29 | C2 | semidirect |
| 7. C29×#504 | C2 | semidirect |
| 15. C29×M32 | C22 | semidirect |
| 16. C2×C16×C29 | C22 | semidirect |
| 17. #11745160 | C22 | semidirect |
| 18. C2×#90768 | C22 | semidirect |
| 21. #11745146 | C22 | semidirect |
| 22. #11745146 | C22 | semidirect |
| 23. C16×D29 | C22 | semidirect |
| 73. #504 | D29 | semidirect |
| 92. M32 | C2×D29 | semidirect |
| 95. C2×C16 | C2×D29 | semidirect |
| 96. C29 | #3407 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #131×D29 | 2 |
| #14271581 | 2 |
| #14271580 | 2 |
| #14271579 | 2 |
| C2×#11745146 | 2 |
| M32×D29 | 2 |
| C29×#504 | 2 |
| #3407 | 29 |