Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
1386 conjugacy classes of subgroups; only the 382 normal subgroups are shown.
This group has 1386 conjugacy classes of subgroups — too many to draw. Only its 382 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×D8×C29 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C29 ◁ C29×#376 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C29×#497 | C2 | semidirect |
| 3. C2×C29×#494 | C2 | semidirect |
| 4. C29×#2658 | C2 | semidirect |
| 5. C29×#1726 | C2 | semidirect |
| 61. #33309 | C29 | direct (N × H) |
| 78. C2×#497 | C2×C29 | semidirect |
| 80. C2×#494 | C2×C29 | semidirect |
| 81. #2658 | C2×C29 | semidirect |
| 82. #1726 | C2×C29 | semidirect |
| 128. C29 | #33309 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#497 | 2 |
| C2×C29×#495 | 2 |
| C2×C29×#494 | 2 |
| C29×#2658 | 2 |
| C29×#1726 | 2 |
| #33309 | 29 |