Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
288 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C29 | #410 |
| commutator | C22×C4 | C22×C4×C29 |
| Frattini, cosocle | C2×M16 | C23×C29 |
| socle | C2×C29 | #1464 |
| prime radical | C2×#41×C29 | C2×C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C29 ◁ C42×C29 ◁ C4×M16×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#2165 | C2 | semidirect |
| 3. C29×#1328 | C2 | semidirect |
| 65. #11524 | C29 | direct (N × H) |
| 88. #2165 | C2×C29 | semidirect |
| 89. #1328 | C2×C29 | semidirect |
| 140. C29 | #11524 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2922 | 2 |
| C29×#2165 | 2 |
| C29×#1328 | 2 |
| C29×#1321 | 2 |
| #11524 | 29 |