Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
1194 conjugacy classes of subgroups; only the 366 normal subgroups are shown.
This group has 1194 conjugacy classes of subgroups — too many to draw. Only its 366 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×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C29 |
| prime radical | C22×D4×C29 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C29 ◁ C43×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#2868 | C2 | semidirect |
| 4. C29×#1981 | C2 | semidirect |
| 5. C29×#1842 | C2 | semidirect |
| 61. C42×C29 | SD16 | semidirect |
| 64. #33162 | C29 | direct (N × H) |
| 87. #2868 | C2×C29 | semidirect |
| 89. #1981 | C2×C29 | semidirect |
| 90. #1842 | C2×C29 | semidirect |
| 100. C4×C29 | #461 | semidirect |
| 140. C29 | #33162 | direct (N × H) |
| 163. C42 | SD16×C29 | semidirect |
| 196. C4 | C29×#461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#461 | 2 |
| C29×#2868 | 2 |
| C42×D4×C29 | 2 |
| C29×#1981 | 2 |
| C29×#1842 | 2 |
| #33162 | 29 |