Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
292 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 128 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 | C2×C4⋊C4 |
| prime radical | C24×C29 | Q8 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C29 ◁ C23×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C29×#108 | C2 | semidirect |
| 4. C29×#341 | C2 | semidirect |
| 44. #1810 | C29 | direct (N × H) |
| 49. C22×C29 | #108 | semidirect |
| 57. C2×#108 | C2×C29 | semidirect |
| 59. #341 | C2×C29 | semidirect |
| 72. C29 | #1810 | direct (N × H) |
| 108. C22 | C29×#108 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C8×C29 | 2 |
| C2×C29×#108 | 2 |
| C29×#407 | 2 |
| C29×#341 | 2 |
| #1810 | 29 |