Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
262 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C29 | #120 |
| commutator | C2×C4 | C22×C4×C29 |
| Frattini, cosocle | C22×C4 | C23×C29 |
| socle | C2×C29 | #385 |
| prime radical | C2×#41×C29 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C29 ◁ C22×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#430 | C2 | semidirect |
| 3. C29×#423 | C2 | semidirect |
| 6. C29×#344 | C2 | semidirect |
| 7. C29×#339 | C2 | semidirect |
| 21. C29×#104 | C4 | semidirect |
| 22. C29×#104 | C4 | semidirect |
| 78. #1861 | C29 | direct (N × H) |
| 94. #430 | C2×C29 | semidirect |
| 95. #423 | C2×C29 | semidirect |
| 98. #344 | C2×C29 | semidirect |
| 99. #339 | C2×C29 | semidirect |
| 118. #104 | C4×C29 | semidirect |
| 119. #104 | C4×C29 | semidirect |
| 120. C29 | #1861 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#568 | 2 |
| C29×#430 | 2 |
| C29×#423 | 2 |
| C29×#421 | 2 |
| C2×C29×#104 | 2 |
| C29×#344 | 2 |
| C29×#339 | 2 |
| #1861 | 29 |