Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
1118 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 1118 conjugacy classes of subgroups — too many to draw. Only its 218 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C29 | #120 |
| commutator | C23 | C22×C8×C29 |
| Frattini, cosocle | C23×C4 | C23×C29 |
| socle | C22×C29 | #379 |
| prime radical | C2×C29×H(5,𝔽2) | C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C29 ◁ C23×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#1869 | C2 | semidirect |
| 3. C29×#1459 | C2 | semidirect |
| 5. C23×C8×C29 | C22 | semidirect |
| 13. C2×C29×C22⋊C8 | C22 | semidirect |
| 18. C29×H(5,𝔽2) | C8 | semidirect |
| 93. #8316 | C29 | direct (N × H) |
| 103. C23×C29 | C22⋊C8 | semidirect |
| 126. C2×C4×C29 | C22⋊C8 | semidirect |
| 132. #1869 | C2×C29 | semidirect |
| 133. #1459 | C2×C29 | semidirect |
| 154. C23×C8 | C22×C29 | semidirect |
| 162. C2×C22⋊C8 | C22×C29 | semidirect |
| 173. H(5,𝔽2) | C8×C29 | semidirect |
| 204. C29 | #8316 | direct (N × H) |
| 258. C23 | C29×C22⋊C8 | semidirect |
| 281. C2×C4 | C29×C22⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C29×H(5,𝔽2) | 2 |
| C29×#1869 | 2 |
| C29×#1459 | 2 |
| #8316 | 29 |