Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
540 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 540 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 | C22×C29 | C23×C4 |
| Fitting | C29×#376 | C2 |
| socle, cosocle | C23×C29 | C24 |
| prime radical | C22×D116 | C22 |
| hypercenter | #376 | D29 |
| hypocenter | C29 | #2319 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ #376 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #14271061 | C2 | semidirect |
| 4. #14271052 | C2 | semidirect |
| 5. #14271025 | C2 | semidirect |
| 6. #14271022 | C2 | semidirect |
| 7. C4×C4⋊Dic29 | C2 | semidirect |
| 8. C29×#376 | C2 | semidirect |
| 20. C4×D116 | C4 | semidirect |
| 98. #376 | D29 | semidirect |
| 122. C29 | #2319 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D116 | 2 |
| #14271065 | 2 |
| #14271061 | 2 |
| #14271052 | 2 |
| #14271025 | 2 |
| #14271022 | 2 |
| C4×C4⋊Dic29 | 2 |
| C29×#376 | 2 |
| #2319 | 29 |