Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
286 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C29 | #120 |
| commutator | C2×C4 | C22×C4×C29 |
| Frattini, cosocle | C22×C4 | C23×C29 |
| prime radical | C2×#41×C29 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C22×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#428 | C2 | semidirect |
| 5. C29×#382 | C2 | semidirect |
| 6. C29×#343 | C2 | semidirect |
| 7. C29×#339 | C2 | semidirect |
| 22. C29×#104 | C4 | semidirect |
| 42. M16×C29 | C2×C4 | semidirect |
| 57. C42×C29 | C2×C4 | semidirect |
| 87. #1860 | C29 | direct (N × H) |
| 107. #428 | C2×C29 | semidirect |
| 110. #382 | C2×C29 | semidirect |
| 111. #343 | C2×C29 | semidirect |
| 112. #339 | C2×C29 | semidirect |
| 133. #104 | C4×C29 | semidirect |
| 137. C29 | #1860 | direct (N × H) |
| 154. M16 | C2×C4×C29 | semidirect |
| 169. C42 | C2×C4×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#520 | 2 |
| C29×#428 | 2 |
| C2×C29×#104 | 2 |
| C29×#417 | 2 |
| C29×#382 | 2 |
| C29×#343 | 2 |
| C29×#339 | 2 |
| #1860 | 29 |