Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
256 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 72 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 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C29 |
| prime radical | C22×D8×C29 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C22×C4×C29 ◁ C22×C8×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C29×SD32 | C2 | semidirect |
| 3. C29×#467 | C2 | semidirect |
| 4. C29×#357 | C2 | semidirect |
| 5. C29×C22⋊C16 | C2 | semidirect |
| 7. C2×Q16×C29 | C22 | semidirect |
| 14. C2×C16×C29 | C22 | semidirect |
| 15. C29×#107 | C22 | semidirect |
| 53. #2187 | C29 | direct (N × H) |
| 60. C22×C29 | SD32 | semidirect |
| 68. C2×SD32 | C2×C29 | semidirect |
| 69. #467 | C2×C29 | semidirect |
| 70. #357 | C2×C29 | semidirect |
| 71. C22⋊C16 | C2×C29 | semidirect |
| 78. C2×Q16 | C22×C29 | semidirect |
| 85. C2×C16 | C22×C29 | semidirect |
| 86. #107 | C22×C29 | semidirect |
| 88. C29 | #2187 | direct (N × H) |
| 131. C22 | C29×SD32 | 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×SD32 | 2 |
| C29×#467 | 2 |
| C29×#357 | 2 |
| C29×C22⋊C16 | 2 |
| #2187 | 29 |