Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
618 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 140 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 | C22×#41×C29 | 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 |
|---|---|---|
| 2. C2×C29×#104 | C2 | semidirect |
| 3. C29×#407 | C2 | semidirect |
| 4. C4×C22⋊C4×C29 | C2 | semidirect |
| 8. C2×#41×C29 | C4 | semidirect |
| 10. C22×Q8×C29 | C4 | semidirect |
| 12. C22×D4×C29 | C4 | semidirect |
| 15. C2×M16×C29 | C22 | semidirect |
| 17. C2×C42×C29 | C22 | semidirect |
| 67. Q8×C29 | C22⋊C4 | semidirect |
| 72. D4×C29 | C22⋊C4 | semidirect |
| 91. #1789 | C29 | direct (N × H) |
| 104. C22×C29 | #104 | semidirect |
| 114. C2×#104 | C2×C29 | semidirect |
| 115. #407 | C2×C29 | semidirect |
| 116. C4×C22⋊C4 | C2×C29 | semidirect |
| 127. C2×#41 | C4×C29 | semidirect |
| 129. C22×Q8 | C4×C29 | semidirect |
| 131. C22×D4 | C4×C29 | semidirect |
| 134. C2×M16 | C22×C29 | semidirect |
| 136. C2×C42 | C22×C29 | semidirect |
| 141. C29 | #1789 | direct (N × H) |
| 187. Q8 | C22⋊C4×C29 | semidirect |
| 192. D4 | C22⋊C4×C29 | semidirect |
| 223. C22 | C29×#104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#41×C29 | 2 |
| C2×C29×#104 | 2 |
| C29×#407 | 2 |
| C4×C22⋊C4×C29 | 2 |
| #1789 | 29 |