Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
1154 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 150 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C29 | C2×#99 |
| commutator | C22×C4 | C22×C4×C29 |
| Frattini, cosocle | C22×Q8 | C23×C29 |
| prime radical | C2×C29×#535 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C22×C4×C29 ◁ C22×#41×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C29×#355 | C2 | semidirect |
| 3. C29×#1785 | C2 | semidirect |
| 12. C2×C29×#101 | C22 | semidirect |
| 91. #12703 | C29 | direct (N × H) |
| 131. C2×#355 | C2×C29 | semidirect |
| 132. #1785 | C2×C29 | semidirect |
| 162. C2×#101 | C22×C29 | semidirect |
| 203. C29 | #12703 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#535 | 2 |
| C2×C29×#355 | 2 |
| C29×#1785 | 2 |
| #12703 | 29 |