Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
340 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C29 | C2×C22⋊C4 |
| commutator | C2×C4 | C22×C4×C29 |
| Frattini, cosocle | C22×C4 | C23×C29 |
| prime radical | C2×C29×#121 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C29×C22⋊C8 | C2 | semidirect |
| 3. C29×#380 | C2 | semidirect |
| 4. C29×#327 | C2 | semidirect |
| 6. C22×D4×C29 | C4 | semidirect |
| 11. C29×#121 | C4 | semidirect |
| 14. C2×C4⋊C4×C29 | C4 | semidirect |
| 18. C29×C22⋊C8 | C22 | semidirect |
| 19. C29×#95 | C22 | semidirect |
| 78. #1519 | C29 | direct (N × H) |
| 103. C2×C22⋊C8 | C2×C29 | semidirect |
| 104. #380 | C2×C29 | semidirect |
| 105. #327 | C2×C29 | semidirect |
| 115. C22×D4 | C4×C29 | semidirect |
| 120. #121 | C4×C29 | semidirect |
| 123. C2×C4⋊C4 | C4×C29 | semidirect |
| 127. C22⋊C8 | C22×C29 | semidirect |
| 128. #95 | C22×C29 | semidirect |
| 129. C29 | #1519 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#121 | 2 |
| C2×C29×C22⋊C8 | 2 |
| C29×#380 | 2 |
| C29×#327 | 2 |
| #1519 | 29 |