Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
164 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 68 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 | C29×#466 | 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 |
|---|---|---|
| 1. C2×C29×SD32 | C2 | semidirect |
| 2. C22×C16×C29 | C2 | semidirect |
| 3. C29×#467 | C2 | semidirect |
| 5. C29×#367 | C2 | semidirect |
| 6. C29×#358 | C2 | semidirect |
| 7. C29×#357 | C2 | semidirect |
| 39. C16×C29 | D4 | semidirect |
| 57. #2217 | C29 | direct (N × H) |
| 63. C22×C29 | SD32 | semidirect |
| 71. C2×SD32 | C2×C29 | semidirect |
| 72. C22×C16 | C2×C29 | semidirect |
| 73. #467 | C2×C29 | semidirect |
| 75. #367 | C2×C29 | semidirect |
| 76. #358 | C2×C29 | semidirect |
| 77. #357 | C2×C29 | semidirect |
| 96. C29 | #2217 | direct (N × H) |
| 115. C16 | D4×C29 | semidirect |
| 138. C22 | C29×SD32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×SD32 | 2 |
| C22×C16×C29 | 2 |
| C29×#467 | 2 |
| C29×#466 | 2 |
| C29×#367 | 2 |
| C29×#358 | 2 |
| C29×#357 | 2 |
| #2217 | 29 |