Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
756 conjugacy classes of subgroups; only the 340 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 340 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C29 | C22×C22⋊C4 |
| commutator | C22 | C23×C4×C29 |
| Frattini, cosocle | C2×C4 | C24×C29 |
| prime radical | C2×C29×H(5,𝔽2) | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C29 ◁ C2×#41×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#568 | C2 | semidirect |
| 3. C29×#413 | C2 | semidirect |
| 4. C2×C29×#100 | C2 | semidirect |
| 12. C2×M16×C29 | C22 | semidirect |
| 13. C29×#101 | C22 | semidirect |
| 14. C29×#100 | C22 | semidirect |
| 48. #2888 | C29 | direct (N × H) |
| 59. #568 | C2×C29 | semidirect |
| 60. #413 | C2×C29 | semidirect |
| 61. C2×#100 | C2×C29 | semidirect |
| 73. C2×M16 | C22×C29 | semidirect |
| 74. #101 | C22×C29 | semidirect |
| 75. #100 | C22×C29 | semidirect |
| 76. C29 | #2888 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×H(5,𝔽2) | 2 |
| C29×#568 | 2 |
| C29×#413 | 2 |
| C2×C29×#100 | 2 |
| #2888 | 29 |