Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
526 conjugacy classes of subgroups; only the 238 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 238 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 | #95 |
| commutator | C23 | C2×C42×C29 |
| Frattini, cosocle | C2×C42 | C23×C29 |
| prime radical | C24×C29 | C42 |
| LCS | G ▷ C23 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C29 ◁ C22×C42×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#1308 | C2 | direct (N × H) |
| 41. C2×#1308 | C29 | direct (N × H) |
| 58. #1308 | C2×C29 | direct (N × H) |
| 78. C2×C29 | #1308 | direct (N × H) |
| 94. C29 | C2×#1308 | direct (N × H) |
| 137. C2 | C29×#1308 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#432 | 2 |
| C29×#1308 | 2 |
| C2×#1308 | 29 |