Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
376 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C29 | C2×D4 |
| commutator | C2×C4 | C22×C4×C29 |
| Frattini, cosocle | C22×C4 | C23×C29 |
| socle | C22×C29 | C2×C22⋊C4 |
| prime radical | C29×#525 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C29 ◁ C23×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×M16×C29 | C2 | semidirect |
| 3. C2×C29×#104 | C2 | semidirect |
| 4. C4×C22⋊C4×C29 | C2 | semidirect |
| 5. C29×#339 | C2 | semidirect |
| 13. C29×C22⋊Q8 | C4 | semidirect |
| 14. C29×C22⋊Q8 | C4 | semidirect |
| 15. C29×#121 | C4 | semidirect |
| 16. C29×#121 | C4 | semidirect |
| 45. M16×C29 | D4 | semidirect |
| 95. #1871 | C29 | direct (N × H) |
| 107. C22×C29 | #104 | semidirect |
| 119. C22×M16 | C2×C29 | semidirect |
| 121. C2×#104 | C2×C29 | semidirect |
| 122. C4×C22⋊C4 | C2×C29 | semidirect |
| 123. #339 | C2×C29 | semidirect |
| 138. C22⋊Q8 | C4×C29 | semidirect |
| 139. C22⋊Q8 | C4×C29 | semidirect |
| 140. #121 | C4×C29 | semidirect |
| 141. #121 | C4×C29 | semidirect |
| 150. C29 | #1871 | direct (N × H) |
| 171. M16 | D4×C29 | semidirect |
| 232. C22 | C29×#104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×M16×C29 | 2 |
| C29×#525 | 2 |
| C2×C29×#104 | 2 |
| C4×C22⋊C4×C29 | 2 |
| C29×#339 | 2 |
| #1871 | 29 |