Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
370 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 92 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 | C22×C4 | C23×C29 |
| prime radical | C29×#537 | C2 |
| LCS | G ▷ C22×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 |
|---|---|---|
| 1. C2×C29×#137 | C2 | semidirect |
| 3. C2×C29×#104 | C2 | semidirect |
| 4. C29×#391 | C2 | semidirect |
| 5. C29×#343 | C2 | semidirect |
| 28. C2×Q8×C29 | D4 | semidirect |
| 40. M16×C29 | D4 | semidirect |
| 73. #2007 | C29 | direct (N × H) |
| 88. C2×#137 | C2×C29 | semidirect |
| 90. C2×#104 | C2×C29 | semidirect |
| 91. #391 | C2×C29 | semidirect |
| 92. #343 | C2×C29 | semidirect |
| 113. C29 | #2007 | direct (N × H) |
| 122. C2×Q8 | D4×C29 | semidirect |
| 134. M16 | D4×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#137 | 2 |
| C29×#537 | 2 |
| C2×C29×#104 | 2 |
| C29×#391 | 2 |
| C29×#343 | 2 |
| #2007 | 29 |