Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
186 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C29 | C2×D4 |
| commutator | C2×C4 | C22×C4×C29 |
| Frattini, cosocle | C22×C4 | C23×C29 |
| socle | C22×C29 | C4×D4 |
| prime radical | C23×C29 | #41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C29 ◁ C22×C8×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 15. C29×#107 | C4 | semidirect |
| 16. C29×#107 | C4 | semidirect |
| 17. C29×#106 | C4 | semidirect |
| 18. C29×#106 | C4 | semidirect |
| 69. #1922 | C29 | direct (N × H) |
| 103. #107 | C4×C29 | semidirect |
| 104. #107 | C4×C29 | semidirect |
| 105. #106 | C4×C29 | semidirect |
| 106. #106 | C4×C29 | semidirect |
| 111. C29 | #1922 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#427 | 2 |
| C29×#424 | 2 |
| C29×#405 | 2 |
| C29×#341 | 2 |
| C29×#339 | 2 |
| C29×#336 | 2 |
| #1922 | 29 |