Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
336 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 76 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 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C29 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C42×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D42×C29 | C2 | semidirect |
| 2. C29×#493 | C2 | semidirect |
| 3. C29×#459 | C2 | semidirect |
| 4. C29×#331 | C2 | semidirect |
| 5. C29×D4⋊C8 | C2 | semidirect |
| 10. C29×#127 | C22 | semidirect |
| 14. C29×C4⋊C8 | C22 | semidirect |
| 16. C4×C8×C29 | C22 | semidirect |
| 48. D4×C29 | D8 | semidirect |
| 56. #1619 | C29 | direct (N × H) |
| 70. D42 | C2×C29 | semidirect |
| 71. #493 | C2×C29 | semidirect |
| 72. #459 | C2×C29 | semidirect |
| 73. #331 | C2×C29 | semidirect |
| 74. D4⋊C8 | C2×C29 | semidirect |
| 84. #127 | C22×C29 | semidirect |
| 88. C4⋊C8 | C22×C29 | semidirect |
| 90. C4×C8 | C22×C29 | semidirect |
| 91. C29 | #1619 | direct (N × H) |
| 123. D4 | D8×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D42×C29 | 2 |
| C29×#493 | 2 |
| C29×#459 | 2 |
| C29×#331 | 2 |
| C29×D4⋊C8 | 2 |
| #1619 | 29 |