Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
440 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 86 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 | #2044 |
| commutator, Frattini, cosocle | C2×#41 | C23×C29 |
| prime radical | C29×#3199 | C2 |
| LCS | G ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C29 ◁ C2×C4×C29 ◁ C2×#41×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#2128 | C2 | semidirect |
| 3. C29×#2122 | C2 | semidirect |
| 4. C29×#1914 | C2 | semidirect |
| 5. C29×#1910 | C2 | semidirect |
| 6. C29×#1868 | C2 | semidirect |
| 7. C29×#1395 | C2 | semidirect |
| 129. #13432 | C29 | direct (N × H) |
| 172. #2128 | C2×C29 | semidirect |
| 173. #2122 | C2×C29 | semidirect |
| 174. #1914 | C2×C29 | semidirect |
| 175. #1910 | C2×C29 | semidirect |
| 176. #1868 | C2×C29 | semidirect |
| 177. #1395 | C2×C29 | semidirect |
| 275. C29 | #13432 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3199 | 2 |
| C29×#2128 | 2 |
| C29×#2122 | 2 |
| C29×#1914 | 2 |
| C29×#1910 | 2 |
| C29×#1868 | 2 |
| C29×#1395 | 2 |
| #13432 | 29 |