Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
156 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 104 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 | C2×D8 |
| commutator | C8 | C22×C4×C29 |
| Frattini, cosocle | C2×C8 | C23×C29 |
| prime radical | C23×C29 | D8 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C22×C4×C29 ◁ C22×C8×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C29×#367 | C2 | semidirect |
| 5. C29×#366 | C2 | semidirect |
| 9. C29×M32 | C4 | semidirect |
| 28. C16×C29 | C2×C4 | semidirect |
| 41. #2159 | C29 | direct (N × H) |
| 55. #367 | C2×C29 | semidirect |
| 56. #366 | C2×C29 | semidirect |
| 64. M32 | C4×C29 | semidirect |
| 71. C29 | #2159 | direct (N × H) |
| 84. C16 | C2×C4×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×M32 | 2 |
| C29×#427 | 2 |
| C2×C29×#107 | 2 |
| C29×#367 | 2 |
| C29×#366 | 2 |
| #2159 | 29 |