Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
186 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 72 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×#498 | C2 | semidirect |
| 2. C29×#494 | C2 | semidirect |
| 3. C29×#487 | C2 | semidirect |
| 7. C29×#322 | C2 | semidirect |
| 54. #1720 | C29 | direct (N × H) |
| 65. #498 | C2×C29 | semidirect |
| 66. #494 | C2×C29 | semidirect |
| 67. #487 | C2×C29 | semidirect |
| 71. #322 | C2×C29 | semidirect |
| 89. C29 | #1720 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#498 | 2 |
| C29×#494 | 2 |
| C29×#487 | 2 |
| C29×#486 | 2 |
| C29×#322 | 2 |
| #1720 | 29 |