Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
568 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 143 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, socle, cosocle | C23×C29 | C24 |
| Fitting | C29×#400 | C2 |
| prime radical | C22×D116 | C22 |
| hypercenter | #400 | D29 |
| hypocenter | C29 | #2398 |
| LCS | G ▷ C23×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ #400 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#11745249 | C2 | semidirect |
| 3. #14271101 | C2 | semidirect |
| 4. #14271092 | C2 | semidirect |
| 7. #14271076 | C2 | semidirect |
| 8. #14271010 | C2 | semidirect |
| 9. #14271010 | C2 | semidirect |
| 10. #14271008 | C2 | semidirect |
| 11. C29×#400 | C2 | semidirect |
| 132. #400 | D29 | semidirect |
| 171. C29 | #2398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745249 | 2 |
| C2×#11745255 | 2 |
| #14271101 | 2 |
| #14271092 | 2 |
| #14271081 | 2 |
| #14271080 | 2 |
| #14271076 | 2 |
| #14271010 | 2 |
| #14271008 | 2 |
| C29×#400 | 2 |
| #2398 | 29 |