Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
542 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 102 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 | C29×#3109 | C2 |
| 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 |
|---|---|---|
| 1. C29×#3246 | C2 | semidirect |
| 2. C29×#3110 | C2 | semidirect |
| 4. C29×#1955 | C2 | semidirect |
| 5. C29×#1531 | C2 | semidirect |
| 6. C29×#1530 | C2 | semidirect |
| 7. C29×#1290 | C2 | semidirect |
| 134. #10027 | C29 | direct (N × H) |
| 178. #3246 | C2×C29 | semidirect |
| 179. #3110 | C2×C29 | semidirect |
| 181. #1955 | C2×C29 | semidirect |
| 182. #1531 | C2×C29 | semidirect |
| 183. #1530 | C2×C29 | semidirect |
| 184. #1290 | C2×C29 | semidirect |
| 289. C29 | #10027 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3246 | 2 |
| C29×#3110 | 2 |
| C29×#3109 | 2 |
| C29×#1955 | 2 |
| C29×#1531 | 2 |
| C29×#1530 | 2 |
| C29×#1290 | 2 |
| #10027 | 29 |