Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
1098 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 1098 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×#532 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C22×C4×C29 ◁ C22×#41×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×#1782 | C2 | semidirect |
| 5. C22×#41×C29 | C4 | semidirect |
| 9. C2×C29×C4⋊Q8 | C4 | semidirect |
| 11. C2×C29×#124 | C4 | semidirect |
| 15. C22×C42×C29 | C4 | semidirect |
| 123. #12695 | C29 | direct (N × H) |
| 173. C2×#354 | C2×C29 | semidirect |
| 174. C2×#353 | C2×C29 | semidirect |
| 175. #1782 | C2×C29 | semidirect |
| 200. C22×#41 | C4×C29 | semidirect |
| 204. C2×C4⋊Q8 | C4×C29 | semidirect |
| 206. C2×#124 | C4×C29 | semidirect |
| 210. C22×C42 | C4×C29 | semidirect |
| 265. C29 | #12695 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#532 | 2 |
| C2×C29×#354 | 2 |
| C2×C29×#353 | 2 |
| C29×#1782 | 2 |
| #12695 | 29 |