Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
342 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 108 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 | #120 |
| commutator | C23 | C22×C4×C29 |
| Frattini, cosocle | C22×C4 | C23×C29 |
| socle | C2×C29 | #386 |
| prime radical | C29×#525 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C29 ◁ C22×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C29×#568 | C2 | semidirect |
| 3. C29×#413 | C2 | semidirect |
| 4. C29×#407 | C2 | semidirect |
| 5. C29×#344 | C2 | semidirect |
| 42. C2×C8×C29 | D4 | semidirect |
| 73. #1891 | C29 | direct (N × H) |
| 90. #568 | C2×C29 | semidirect |
| 92. #413 | C2×C29 | semidirect |
| 93. #407 | C2×C29 | semidirect |
| 94. #344 | C2×C29 | semidirect |
| 115. C29 | #1891 | direct (N × H) |
| 137. C2×C8 | D4×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#568 | 2 |
| C29×#525 | 2 |
| C29×#413 | 2 |
| C29×#407 | 2 |
| C29×#344 | 2 |
| #1891 | 29 |