Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
564 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 189 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 | C22×C42×C29 | C2 |
| prime radical | C24×C29 | C23 |
| hypercenter | C22×C42 | D29 |
| hypocenter | C29 | #2855 |
| LCS | G ▷ C23×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ C22×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14271069 | C2 | semidirect |
| 3. #14271061 | C2 | semidirect |
| 4. #14271047 | C2 | semidirect |
| 34. C22×C4×C29 | Q8 | semidirect |
| 129. C29 | #2855 | semidirect |
| 141. C22×C4 | Dic58 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745286 | 2 |
| #14271069 | 2 |
| #14271061 | 2 |
| #14271047 | 2 |
| #14271036 | 2 |
| #14271026 | 2 |
| #14271023 | 2 |
| C22×C42×C29 | 2 |
| #2855 | 29 |