Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1160 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 1160 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×#381 | C2 |
| socle, cosocle | C23×C29 | C24 |
| prime radical | C23×D116 | C2 |
| hypercenter | #381 | D29 |
| hypocenter | C29 | #2308 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ #381 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C22⋊C4×D29 | C2 | semidirect |
| 3. #14271041 | C2 | semidirect |
| 4. #14271026 | C2 | semidirect |
| 5. #14271018 | C2 | semidirect |
| 6. C29×#381 | C2 | semidirect |
| 11. C22×D116 | C4 | semidirect |
| 13. C22×C4×D29 | C22 | semidirect |
| 16. C2×#90781 | C22 | semidirect |
| 17. C2×#90781 | C22 | semidirect |
| 19. C29×#95 | C22 | semidirect |
| 20. #11745179 | C22 | semidirect |
| 26. C23×D29 | C2×C4 | semidirect |
| 31. C22×C4×C29 | C2×C4 | semidirect |
| 38. C2×D116 | C2×C4 | semidirect |
| 57. C22×D29 | C22⋊C4 | semidirect |
| 94. #381 | D29 | semidirect |
| 115. #95 | C2×D29 | semidirect |
| 116. C29 | #2308 | semidirect |
| 134. C22×C4 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D116 | 2 |
| C2×C22⋊C4×D29 | 2 |
| #14271041 | 2 |
| #14271026 | 2 |
| #14271018 | 2 |
| C29×#381 | 2 |
| #2308 | 29 |