Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
444 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 112 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 | C2×C4 | C22×C4×C29 |
| Frattini, cosocle | C22×C4 | C23×C29 |
| prime radical | C2×C29×#127 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C22×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#518 | C2 | semidirect |
| 3. C29×#418 | C2 | semidirect |
| 4. C2×C29×#100 | C2 | semidirect |
| 5. C29×#339 | C2 | semidirect |
| 11. C29×#127 | C4 | semidirect |
| 28. C2×D4×C29 | C2×C4 | semidirect |
| 36. C4⋊C4×C29 | D4 | semidirect |
| 41. C42×C29 | C2×C4 | semidirect |
| 65. #1887 | C29 | direct (N × H) |
| 83. #518 | C2×C29 | semidirect |
| 84. #418 | C2×C29 | semidirect |
| 85. C2×#100 | C2×C29 | semidirect |
| 86. #339 | C2×C29 | semidirect |
| 98. #127 | C4×C29 | semidirect |
| 105. C29 | #1887 | direct (N × H) |
| 116. C2×D4 | C2×C4×C29 | semidirect |
| 124. C4⋊C4 | D4×C29 | semidirect |
| 129. C42 | C2×C4×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#127 | 2 |
| C29×#518 | 2 |
| C29×#418 | 2 |
| C2×C29×#100 | 2 |
| C29×#339 | 2 |
| #1887 | 29 |