Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
672 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 280 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 | C25×C29 | C22 |
| 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×#388 | C2 | semidirect |
| 3. C29×#380 | C2 | semidirect |
| 5. C4×C22⋊C4×C29 | C2 | semidirect |
| 9. C2×C4⋊C4×C29 | C22 | semidirect |
| 10. C2×C22⋊C4×C29 | C4 | semidirect |
| 15. C2×C42×C29 | C22 | semidirect |
| 16. C29×#95 | C22 | semidirect |
| 17. C29×#95 | C22 | semidirect |
| 59. #2312 | C29 | direct (N × H) |
| 77. #388 | C2×C29 | semidirect |
| 78. #380 | C2×C29 | semidirect |
| 80. C4×C22⋊C4 | C2×C29 | semidirect |
| 90. C2×C4⋊C4 | C22×C29 | semidirect |
| 91. C2×C22⋊C4 | C4×C29 | semidirect |
| 96. C2×C42 | C22×C29 | semidirect |
| 97. #95 | C22×C29 | semidirect |
| 98. #95 | C22×C29 | semidirect |
| 99. C29 | #2312 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊C4×C29 | 2 |
| C29×#388 | 2 |
| C29×#380 | 2 |
| C29×#379 | 2 |
| C4×C22⋊C4×C29 | 2 |
| #2312 | 29 |