Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
128 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C29 | #102 |
| commutator | C8 | C42×C29 |
| Frattini, cosocle | C22×C8 | C22×C29 |
| socle | C2×C29 | #340 |
| prime radical | C23×C29 | SD16 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C29 ◁ C22×C4×C29 ◁ C22×C8×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. C29×M32 | C4 | semidirect |
| 11. C29×#108 | C4 | semidirect |
| 41. #1389 | C29 | direct (N × H) |
| 62. M32 | C4×C29 | semidirect |
| 65. #108 | C4×C29 | semidirect |
| 68. C29 | #1389 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×M32 | 2 |
| C2×C29×#108 | 2 |
| C29×#427 | 2 |
| #1389 | 29 |