Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
198 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 80 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 | #127 |
| commutator, Frattini, cosocle | C42 | C23×C29 |
| prime radical | C29×#127 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C42×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C29×#500 | C2 | semidirect |
| 2. C29×#498 | C2 | semidirect |
| 5. C29×#487 | C2 | semidirect |
| 7. C29×#322 | C2 | semidirect |
| 54. C8×C29 | SD16 | semidirect |
| 55. #1714 | C29 | direct (N × H) |
| 66. #500 | C2×C29 | semidirect |
| 67. #498 | C2×C29 | semidirect |
| 70. #487 | C2×C29 | semidirect |
| 72. #322 | C2×C29 | semidirect |
| 90. C29 | #1714 | direct (N × H) |
| 124. C8 | SD16×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#500 | 2 |
| C29×#498 | 2 |
| C29×#492 | 2 |
| C29×#487 | 2 |
| C29×#486 | 2 |
| C29×#322 | 2 |
| #1714 | 29 |