Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1144 conjugacy classes of subgroups; only the 440 normal subgroups are shown.
This group has 1144 conjugacy classes of subgroups — too many to draw. Only its 440 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C29 | C23 |
| commutator | C22 | C23×C4×C29 |
| Frattini, cosocle | C23 | C24×C29 |
| prime radical | C25×C29 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C29×#381 | C2 | direct (N × H) |
| 4. C2×C29×#95 | C2 | semidirect |
| 7. C23×C4×C29 | C4 | semidirect |
| 13. C29×#95 | C22 | semidirect |
| 25. C22×C4×C29 | C2×C4 | semidirect |
| 46. C2×#381 | C29 | direct (N × H) |
| 61. #381 | C2×C29 | direct (N × H) |
| 62. C2×#95 | C2×C29 | semidirect |
| 64. C2×C29 | #381 | direct (N × H) |
| 70. C23×C4 | C4×C29 | semidirect |
| 76. #95 | C22×C29 | semidirect |
| 77. C29 | C2×#381 | direct (N × H) |
| 89. C22×C4 | C2×C4×C29 | semidirect |
| 123. C2 | C29×#381 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C4×C29 | 2 |
| C22×C22⋊C4×C29 | 2 |
| C29×#381 | 2 |
| C2×C29×#95 | 2 |
| C2×#381 | 29 |