Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
4614 conjugacy classes of subgroups; only the 734 normal subgroups are shown.
This group has 4614 conjugacy classes of subgroups — too many to draw. Only its 734 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C29 | C23 |
| commutator | C23 | C23×C4×C29 |
| Frattini, cosocle | C24 | C24×C29 |
| socle | C24×C29 | C24 |
| prime radical | C23×#41×C29 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4×C22⋊C4×C29 | C2 | semidirect |
| 3. C29×#1446 | C2 | semidirect |
| 4. C29×#1438 | C2 | semidirect |
| 6. C22×#41×C29 | C4 | semidirect |
| 48. C22×C4×C29 | C22⋊C4 | semidirect |
| 53. C22×C4×C29 | #41 | semidirect |
| 56. #13851 | C29 | direct (N × H) |
| 80. C2×C4×C22⋊C4 | C2×C29 | semidirect |
| 81. #1446 | C2×C29 | semidirect |
| 82. #1438 | C2×C29 | semidirect |
| 96. C22×#41 | C4×C29 | semidirect |
| 126. C29 | #13851 | direct (N × H) |
| 143. C22×C4 | C22⋊C4×C29 | semidirect |
| 148. C22×C4 | #41×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#41×C29 | 2 |
| C2×C4×C22⋊C4×C29 | 2 |
| C29×#1446 | 2 |
| C29×#1438 | 2 |
| #13851 | 29 |