Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
336 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C29 | C22⋊C4 |
| commutator | C2×C4 | C22×C4×C29 |
| Frattini, cosocle | C22×C4 | C23×C29 |
| prime radical | C24×C29 | D4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C29 ◁ C23×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C29×#328 | C2 | direct (N × H) |
| 5. C22×Q8×C29 | C4 | semidirect |
| 11. C29×C22⋊Q8 | C4 | semidirect |
| 14. C2×C4⋊C4×C29 | C4 | semidirect |
| 23. C2×Q8×C29 | C2×C4 | semidirect |
| 42. C4⋊C4×C29 | C2×C4 | semidirect |
| 73. C2×#328 | C29 | direct (N × H) |
| 97. #328 | C2×C29 | direct (N × H) |
| 101. C2×C29 | #328 | direct (N × H) |
| 105. C22×Q8 | C4×C29 | semidirect |
| 111. C22⋊Q8 | C4×C29 | semidirect |
| 114. C2×C4⋊C4 | C4×C29 | semidirect |
| 120. C29 | C2×#328 | direct (N × H) |
| 124. C2×Q8 | C2×C4×C29 | semidirect |
| 143. C4⋊C4 | C2×C4×C29 | semidirect |
| 197. C2 | C29×#328 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×C22⋊Q8 | 2 |
| C2×C29×C22⋊C8 | 2 |
| C2×C29×#95 | 2 |
| C29×#328 | 2 |
| C2×#328 | 29 |