Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
688 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 213 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, prime radical | C2×C29×#120 | C2 |
| socle, cosocle | C23×C29 | C24 |
| hypercenter | C2×#120 | D29 |
| hypocenter | C29 | #2375 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ C2×#120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14271066 | C2 | semidirect |
| 2. #14271056 | C2 | semidirect |
| 3. #14271043 | C2 | semidirect |
| 4. #14271019 | C2 | semidirect |
| 8. C23×Dic29 | C22 | semidirect |
| 9. C29×#120 | C4 | semidirect |
| 13. C2×C22⋊Dic29 | C22 | semidirect |
| 14. C2×C4⋊Dic29 | C22 | semidirect |
| 15. C2×C4×Dic29 | C22 | semidirect |
| 16. #11745179 | C22 | semidirect |
| 19. C24×C29 | C2×C4 | semidirect |
| 29. C22⋊C4×C29 | C2×C4 | semidirect |
| 85. #120 | Dic29 | semidirect |
| 93. C29 | #2375 | semidirect |
| 96. C24 | C2×Dic29 | semidirect |
| 110. C22⋊C4 | C2×Dic29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271066 | 2 |
| #14271056 | 2 |
| #14271043 | 2 |
| #14271019 | 2 |
| C2×C29×#120 | 2 |
| #2375 | 29 |