Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
514 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 176 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 ◁ C23×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C29×#121 | C2 | semidirect |
| 2. C29×#481 | C2 | semidirect |
| 3. C29×#469 | C2 | semidirect |
| 4. C29×#447 | C2 | semidirect |
| 5. C29×#407 | C2 | semidirect |
| 7. C22×D4×C29 | C22 | semidirect |
| 9. C2×D8×C29 | C22 | semidirect |
| 10. C2×M16×C29 | C22 | semidirect |
| 14. C29×#121 | C22 | semidirect |
| 15. C2×C4⋊C4×C29 | C22 | semidirect |
| 17. C29×#106 | C22 | semidirect |
| 18. C29×#102 | C22 | semidirect |
| 19. C29×C22⋊C8 | C22 | semidirect |
| 63. #3192 | C29 | direct (N × H) |
| 79. C2×#121 | C2×C29 | semidirect |
| 80. #481 | C2×C29 | semidirect |
| 81. #469 | C2×C29 | semidirect |
| 82. #447 | C2×C29 | semidirect |
| 83. #407 | C2×C29 | semidirect |
| 90. C22×D4 | C22×C29 | semidirect |
| 92. C2×D8 | C22×C29 | semidirect |
| 93. C2×M16 | C22×C29 | semidirect |
| 97. #121 | C22×C29 | semidirect |
| 98. C2×C4⋊C4 | C22×C29 | semidirect |
| 100. #106 | C22×C29 | semidirect |
| 101. #102 | C22×C29 | semidirect |
| 102. C22⋊C8 | C22×C29 | semidirect |
| 103. C29 | #3192 | 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 |
| C29×#481 | 2 |
| C29×#469 | 2 |
| C29×#447 | 2 |
| C29×#407 | 2 |
| #3192 | 29 |