Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
442 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 90 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 | #447 |
| commutator, Frattini, cosocle | C4×C8 | C23×C29 |
| prime radical | D4×D8×C29 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C42×C29 ◁ C8×D4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#2248 | C2 | semidirect |
| 3. C29×#2208 | C2 | semidirect |
| 4. C29×#1669 | C2 | semidirect |
| 5. C29×#1361 | C2 | semidirect |
| 6. C29×#1331 | C2 | semidirect |
| 7. C29×D4⋊C16 | C2 | semidirect |
| 12. C29×#494 | C22 | semidirect |
| 20. C29×C4⋊C16 | C22 | semidirect |
| 22. C4×C16×C29 | C22 | semidirect |
| 23. C29×#335 | C22 | semidirect |
| 96. #12320 | C29 | direct (N × H) |
| 115. D4×C29 | SD32 | semidirect |
| 132. #2248 | C2×C29 | semidirect |
| 133. #2208 | C2×C29 | semidirect |
| 134. #1669 | C2×C29 | semidirect |
| 135. #1361 | C2×C29 | semidirect |
| 136. #1331 | C2×C29 | semidirect |
| 137. D4⋊C16 | C2×C29 | semidirect |
| 161. #494 | C22×C29 | semidirect |
| 169. C4⋊C16 | C22×C29 | semidirect |
| 171. C4×C16 | C22×C29 | semidirect |
| 172. #335 | C22×C29 | semidirect |
| 211. C29 | #12320 | direct (N × H) |
| 270. D4 | C29×SD32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D8×C29 | 2 |
| C29×#2248 | 2 |
| C29×#2208 | 2 |
| C29×#1669 | 2 |
| C29×#1361 | 2 |
| C29×#1331 | 2 |
| C29×D4⋊C16 | 2 |
| #12320 | 29 |