Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
364 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 180 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C29 | C2×D8 |
| commutator, Frattini, cosocle | C8 | C24×C29 |
| socle | C2×C29 | C22×D8 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C29 ◁ C22×C4×C29 ◁ C22×C8×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C29×#135 | C2 | semidirect |
| 2. C29×#510 | C2 | semidirect |
| 3. C29×#509 | C2 | semidirect |
| 4. C29×#508 | C2 | semidirect |
| 5. C2×C29×M32 | C2 | semidirect |
| 10. C29×#135 | C22 | semidirect |
| 11. C2×Q16×C29 | C22 | semidirect |
| 13. C2×D8×C29 | C22 | semidirect |
| 15. C29×Q32 | C22 | semidirect |
| 16. C29×SD32 | C22 | semidirect |
| 17. C29×D16 | C22 | semidirect |
| 18. C29×M32 | C22 | semidirect |
| 19. C2×C16×C29 | C22 | semidirect |
| 58. #3414 | C29 | direct (N × H) |
| 68. C2×#135 | C2×C29 | semidirect |
| 69. #510 | C2×C29 | semidirect |
| 70. #509 | C2×C29 | semidirect |
| 71. #508 | C2×C29 | semidirect |
| 72. C2×M32 | C2×C29 | semidirect |
| 81. #135 | C22×C29 | semidirect |
| 82. C2×Q16 | C22×C29 | semidirect |
| 84. C2×D8 | C22×C29 | semidirect |
| 86. Q32 | C22×C29 | semidirect |
| 87. SD32 | C22×C29 | semidirect |
| 88. D16 | C22×C29 | semidirect |
| 89. M32 | C22×C29 | semidirect |
| 90. C2×C16 | C22×C29 | semidirect |
| 91. C29 | #3414 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#135 | 2 |
| C29×#510 | 2 |
| C29×#509 | 2 |
| C29×#508 | 2 |
| C2×C29×M32 | 2 |
| #3414 | 29 |