Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
456 conjugacy classes of subgroups; only the 264 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 264 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C29 | C24 |
| commutator | C22 | C23×C4×C29 |
| Frattini, cosocle | C23 | C24×C29 |
| prime radical | C24×C29 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#389 | C2 | semidirect |
| 4. C29×#387 | C2 | semidirect |
| 6. C29×#384 | C2 | semidirect |
| 7. C29×#383 | C2 | semidirect |
| 9. C29×#126 | C4 | semidirect |
| 33. C4⋊C4×C29 | C2×C4 | semidirect |
| 37. C42×C29 | C2×C4 | semidirect |
| 56. #2383 | C29 | direct (N × H) |
| 70. #389 | C2×C29 | semidirect |
| 72. #387 | C2×C29 | semidirect |
| 74. #384 | C2×C29 | semidirect |
| 75. #383 | C2×C29 | semidirect |
| 81. #126 | C4×C29 | semidirect |
| 94. C29 | #2383 | direct (N × H) |
| 106. C4⋊C4 | C2×C4×C29 | semidirect |
| 110. C42 | 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×#126 | 2 |
| C29×#389 | 2 |
| C29×#388 | 2 |
| C29×#387 | 2 |
| C29×#385 | 2 |
| C29×#384 | 2 |
| C29×#383 | 2 |
| #2383 | 29 |