Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
412 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 128 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 | C2×D4 |
| commutator | C2×C4 | C22×C4×C29 |
| Frattini, cosocle | C22×C4 | C23×C29 |
| prime radical | C2×C29×#121 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C29 ◁ C23×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×M16×C29 | C2 | semidirect |
| 3. C2×C29×#102 | C2 | semidirect |
| 4. C29×#380 | C2 | semidirect |
| 5. C29×#340 | C2 | semidirect |
| 13. C29×#121 | C4 | semidirect |
| 39. C2×C8×C29 | D4 | semidirect |
| 76. #1895 | C29 | direct (N × H) |
| 98. C22×M16 | C2×C29 | semidirect |
| 100. C2×#102 | C2×C29 | semidirect |
| 101. #380 | C2×C29 | semidirect |
| 102. #340 | C2×C29 | semidirect |
| 117. #121 | C4×C29 | semidirect |
| 124. C29 | #1895 | direct (N × H) |
| 144. C2×C8 | D4×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×M16×C29 | 2 |
| C2×C29×#121 | 2 |
| C2×C29×#102 | 2 |
| C29×#380 | 2 |
| C29×#340 | 2 |
| #1895 | 29 |