Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
398 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C29 | C22⋊C4 |
| commutator | C2×C4 | C22×C8×C29 |
| Frattini, cosocle | C22×C8 | C23×C29 |
| socle | C22×C29 | C2×C22⋊C8 |
| prime radical | C29×#525 | C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C29 ◁ C23×C8×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C29×C22⋊C16 | C2 | semidirect |
| 3. C29×#1323 | C2 | semidirect |
| 4. C29×#1315 | C2 | semidirect |
| 76. #11468 | C29 | direct (N × H) |
| 105. C2×C22⋊C16 | C2×C29 | semidirect |
| 106. #1323 | C2×C29 | semidirect |
| 107. #1315 | C2×C29 | semidirect |
| 165. C29 | #11468 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2929 | 2 |
| C2×C29×C22⋊C16 | 2 |
| C29×#1323 | 2 |
| C29×#1315 | 2 |
| #11468 | 29 |