Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
1162 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 1162 conjugacy classes of subgroups — too many to draw. Only its 182 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 | C2×#102 |
| commutator | C2×C8 | C22×C4×C29 |
| Frattini, cosocle | C22×C8 | C23×C29 |
| prime radical | C23×D8×C29 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C23×C4×C29 ◁ C23×C8×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C29×#361 | C2 | semidirect |
| 3. C29×#2112 | C2 | semidirect |
| 4. C29×#1810 | C2 | semidirect |
| 12. C2×C29×M32 | C22 | semidirect |
| 13. C2×C29×#108 | C22 | semidirect |
| 79. #12736 | C29 | direct (N × H) |
| 109. C2×#361 | C2×C29 | semidirect |
| 110. #2112 | C2×C29 | semidirect |
| 111. #1810 | C2×C29 | semidirect |
| 120. C22×C29 | #361 | semidirect |
| 134. C2×M32 | C22×C29 | semidirect |
| 135. C2×#108 | C22×C29 | semidirect |
| 171. C29 | #12736 | direct (N × H) |
| 243. C22 | C29×#361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D8×C29 | 2 |
| C2×C29×#361 | 2 |
| C29×#2112 | 2 |
| C29×#1810 | 2 |
| #12736 | 29 |