Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
368 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 184 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C29 | D8 |
| commutator, Frattini, cosocle | C8 | C24×C29 |
| socle | C22×C29 | C2×D8 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×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×#508 | C2 | direct (N × H) |
| 3. C2×C29×Q32 | C2 | semidirect |
| 4. C2×C29×SD32 | C2 | semidirect |
| 5. C2×C29×D16 | C2 | semidirect |
| 6. C22×C16×C29 | C2 | semidirect |
| 9. C29×#135 | C22 | semidirect |
| 14. C29×Q32 | C22 | semidirect |
| 15. C29×SD32 | C22 | semidirect |
| 16. C29×D16 | C22 | semidirect |
| 19. C2×C16×C29 | C22 | semidirect |
| 54. C2×#508 | C29 | direct (N × H) |
| 64. C2×#135 | C2×C29 | semidirect |
| 65. #508 | C2×C29 | direct (N × H) |
| 66. C2×Q32 | C2×C29 | semidirect |
| 67. C2×SD32 | C2×C29 | semidirect |
| 68. C2×D16 | C2×C29 | semidirect |
| 69. C22×C16 | C2×C29 | semidirect |
| 72. C2×C29 | #508 | direct (N × H) |
| 76. #135 | C22×C29 | semidirect |
| 81. Q32 | C22×C29 | semidirect |
| 82. SD32 | C22×C29 | semidirect |
| 83. D16 | C22×C29 | semidirect |
| 86. C2×C16 | C22×C29 | semidirect |
| 87. C29 | C2×#508 | direct (N × H) |
| 133. C2 | C29×#508 | 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×#508 | 2 |
| C2×C29×Q32 | 2 |
| C2×C29×SD32 | 2 |
| C2×C29×D16 | 2 |
| C22×C16×C29 | 2 |
| C2×#508 | 29 |