Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
1072 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 230 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×#120 |
| commutator, Frattini, cosocle | C42 | C24×C29 |
| prime radical | C29×#3549 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#3152 | C2 | semidirect |
| 3. C29×#3141 | C2 | semidirect |
| 4. C29×#1659 | C2 | semidirect |
| 5. C29×#1525 | C2 | semidirect |
| 6. C29×#1525 | C2 | semidirect |
| 17. C2×C29×C4⋊Q8 | C22 | semidirect |
| 18. C29×#497 | C22 | semidirect |
| 21. C29×#489 | C22 | semidirect |
| 25. C4×M16×C29 | C22 | semidirect |
| 26. C4×M16×C29 | C22 | semidirect |
| 27. C29×#329 | C22 | semidirect |
| 28. C29×#329 | C22 | semidirect |
| 117. #19074 | C29 | direct (N × H) |
| 151. #3152 | C2×C29 | semidirect |
| 152. #3141 | C2×C29 | semidirect |
| 153. #1659 | C2×C29 | semidirect |
| 154. #1525 | C2×C29 | semidirect |
| 155. #1525 | C2×C29 | semidirect |
| 182. C2×C4⋊Q8 | C22×C29 | semidirect |
| 183. #497 | C22×C29 | semidirect |
| 186. #489 | C22×C29 | semidirect |
| 190. C4×M16 | C22×C29 | semidirect |
| 191. C4×M16 | C22×C29 | semidirect |
| 192. #329 | C22×C29 | semidirect |
| 193. #329 | C22×C29 | semidirect |
| 243. C29 | #19074 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3549 | 2 |
| C29×#3152 | 2 |
| C29×#3141 | 2 |
| C29×#1659 | 2 |
| C29×#1525 | 2 |
| #19074 | 29 |