Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
512 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 512 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, socle | C22×C29 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C29 |
| prime radical | C22×D4×C29 | D4 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#3113 | C2 | semidirect |
| 5. C29×#1515 | C2 | semidirect |
| 6. C29×#1491 | C2 | semidirect |
| 7. C29×#1288 | C2 | semidirect |
| 131. #10024 | C29 | direct (N × H) |
| 172. #3113 | C2×C29 | semidirect |
| 175. #1515 | C2×C29 | semidirect |
| 176. #1491 | C2×C29 | semidirect |
| 177. #1288 | C2×C29 | semidirect |
| 277. C29 | #10024 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3140 | 2 |
| C29×#3113 | 2 |
| C29×#2632 | 2 |
| C29×#1533 | 2 |
| C29×#1515 | 2 |
| C29×#1491 | 2 |
| C29×#1288 | 2 |
| #10024 | 29 |