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 | C22×C4×C29 | C22⋊C4 |
| commutator | C2×C4 | C2×C16×C29 |
| Frattini, cosocle | C2×C4×C8 | C22×C29 |
| socle | C23×C29 | C22⋊C8 |
| prime radical | C22×D4×C29 | C8 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C29 ◁ C2×C4×C8×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#1374 | C2 | semidirect |
| 28. C2×D4×C29 | C16 | semidirect |
| 48. #7102 | C29 | direct (N × H) |
| 76. #1374 | C2×C29 | semidirect |
| 121. C29 | #7102 | direct (N × H) |
| 126. C2×D4 | C16×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#1954 | 2 |
| C29×#1374 | 2 |
| #7102 | 29 |