Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
524 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 200 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 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C29 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C2×#41×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×D8×C29 | C2 | semidirect |
| 2. C2×C29×#131 | C2 | semidirect |
| 3. C29×#535 | C2 | semidirect |
| 4. C29×#469 | C2 | semidirect |
| 5. C29×#466 | C2 | semidirect |
| 6. C29×#427 | C2 | semidirect |
| 7. C29×#418 | C2 | semidirect |
| 15. C2×M16×C29 | C22 | semidirect |
| 17. C22×C8×C29 | C22 | semidirect |
| 20. C29×#121 | C22 | semidirect |
| 23. C29×#107 | C22 | semidirect |
| 24. C29×#106 | C22 | semidirect |
| 25. C29×#102 | C22 | semidirect |
| 44. C2×C8×C29 | D4 | semidirect |
| 75. #3058 | C29 | direct (N × H) |
| 89. C22×D8 | C2×C29 | semidirect |
| 90. C2×#131 | C2×C29 | semidirect |
| 91. #535 | C2×C29 | semidirect |
| 92. #469 | C2×C29 | semidirect |
| 93. #466 | C2×C29 | semidirect |
| 94. #427 | C2×C29 | semidirect |
| 95. #418 | C2×C29 | semidirect |
| 108. C2×M16 | C22×C29 | semidirect |
| 110. C22×C8 | C22×C29 | semidirect |
| 113. #121 | C22×C29 | semidirect |
| 116. #107 | C22×C29 | semidirect |
| 117. #106 | C22×C29 | semidirect |
| 118. #102 | C22×C29 | semidirect |
| 119. C29 | #3058 | direct (N × H) |
| 138. 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×D8×C29 | 2 |
| C2×C29×#131 | 2 |
| C29×#535 | 2 |
| C29×#469 | 2 |
| C29×#466 | 2 |
| C29×#427 | 2 |
| C29×#418 | 2 |
| #3058 | 29 |