Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
1214 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 1214 conjugacy classes of subgroups — too many to draw. Only its 150 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×#99 |
| commutator | C22×C4 | C22×C4×C29 |
| Frattini, cosocle | C22×D4 | C23×C29 |
| prime radical | C2×C29×#535 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C24×C29 ◁ C23×D4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C29×#354 | C2 | semidirect |
| 3. C2×C29×#353 | C2 | semidirect |
| 4. C29×#1781 | C2 | semidirect |
| 5. C22×#41×C29 | C4 | semidirect |
| 9. C2×C29×#127 | C4 | semidirect |
| 11. C2×C29×#124 | C4 | semidirect |
| 15. C2×C29×#117 | C4 | semidirect |
| 76. C2×Q8×C29 | C22⋊C4 | semidirect |
| 98. C2×D4×C29 | C22⋊C4 | semidirect |
| 123. C42×C29 | C22⋊C4 | semidirect |
| 124. C42×C29 | C22⋊C4 | semidirect |
| 125. #12696 | C29 | direct (N × H) |
| 180. C2×#354 | C2×C29 | semidirect |
| 181. C2×#353 | C2×C29 | semidirect |
| 182. #1781 | C2×C29 | semidirect |
| 211. C22×#41 | C4×C29 | semidirect |
| 215. C2×#127 | C4×C29 | semidirect |
| 217. C2×#124 | C4×C29 | semidirect |
| 221. C2×#117 | C4×C29 | semidirect |
| 277. C29 | #12696 | direct (N × H) |
| 291. C2×Q8 | C22⋊C4×C29 | semidirect |
| 313. C2×D4 | C22⋊C4×C29 | semidirect |
| 338. C42 | C22⋊C4×C29 | semidirect |
| 339. C42 | C22⋊C4×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#535 | 2 |
| C2×C29×#354 | 2 |
| C2×C29×#353 | 2 |
| C29×#1781 | 2 |
| #12696 | 29 |