Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
688 conjugacy classes of subgroups; only the 264 normal subgroups are shown.
This group has 688 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 | C2×C29×#120 | C2 |
| 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×#390 | C2 | semidirect |
| 3. C29×#388 | C2 | semidirect |
| 4. C29×#386 | C2 | semidirect |
| 5. C29×#379 | C2 | semidirect |
| 8. C23×C4×C29 | C22 | semidirect |
| 9. C29×#120 | C4 | semidirect |
| 10. C2×C4⋊C4×C29 | C22 | semidirect |
| 14. C2×C22⋊C4×C29 | C22 | semidirect |
| 15. C2×C42×C29 | C22 | semidirect |
| 16. C29×#95 | C22 | semidirect |
| 19. C24×C29 | C2×C4 | semidirect |
| 33. C22⋊C4×C29 | C2×C4 | semidirect |
| 56. #2375 | C29 | direct (N × H) |
| 73. #390 | C2×C29 | semidirect |
| 74. #388 | C2×C29 | semidirect |
| 75. #386 | C2×C29 | semidirect |
| 76. #379 | C2×C29 | semidirect |
| 84. C23×C4 | C22×C29 | semidirect |
| 85. #120 | C4×C29 | semidirect |
| 86. C2×C4⋊C4 | C22×C29 | semidirect |
| 90. C2×C22⋊C4 | C22×C29 | semidirect |
| 91. C2×C42 | C22×C29 | semidirect |
| 92. #95 | C22×C29 | semidirect |
| 93. C29 | #2375 | direct (N × H) |
| 96. C24 | C2×C4×C29 | semidirect |
| 110. C22⋊C4 | 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×#120 | 2 |
| C29×#390 | 2 |
| C29×#388 | 2 |
| C29×#386 | 2 |
| C29×#379 | 2 |
| #2375 | 29 |