Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
316 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C29 | #2067 |
| commutator, Frattini, cosocle | C22×C8 | C23×C29 |
| prime radical | C22×D8×C29 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C29 ◁ C22×C4×C29 ◁ C29×#405 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C29×#2161 | C2 | semidirect |
| 2. C29×#2153 | C2 | semidirect |
| 6. C29×#1953 | C2 | semidirect |
| 7. C29×#1385 | C2 | semidirect |
| 88. #13472 | C29 | direct (N × H) |
| 113. #2161 | C2×C29 | semidirect |
| 114. #2153 | C2×C29 | semidirect |
| 118. #1953 | C2×C29 | semidirect |
| 119. #1385 | C2×C29 | semidirect |
| 183. C29 | #13472 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2161 | 2 |
| C29×#2153 | 2 |
| C2×C29×#361 | 2 |
| C29×#1978 | 2 |
| C29×#1953 | 2 |
| C29×#1385 | 2 |
| #13472 | 29 |