Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
374 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 158 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C29 | C2×D8 |
| commutator | C2×C8 | C22×C4×C29 |
| Frattini, cosocle | C22×C8 | C23×C29 |
| socle | C22×C29 | C2×#107 |
| prime radical | C24×C29 | Q16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C29 ◁ C23×C4×C29 ◁ C23×C8×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C29×#368 | C2 | semidirect |
| 4. C29×#1381 | C2 | semidirect |
| 51. #12838 | C29 | direct (N × H) |
| 71. C2×#368 | C2×C29 | semidirect |
| 73. #1381 | C2×C29 | semidirect |
| 113. C29 | #12838 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C29×M32 | 2 |
| C2×C29×#368 | 2 |
| C29×#1810 | 2 |
| C29×#1381 | 2 |
| #12838 | 29 |