Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
944 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C29 | #120 |
| commutator, Frattini, cosocle | C23×C4 | C23×C29 |
| prime radical | C29×#2656 | C2 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C29 ◁ C23×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C29×#448 | C2 | semidirect |
| 3. C2×C29×#327 | C2 | semidirect |
| 4. C29×#1446 | C2 | semidirect |
| 5. C29×#1280 | C2 | semidirect |
| 24. C22×Q8×C29 | D4 | semidirect |
| 47. C29×C22⋊C8 | D4 | semidirect |
| 86. C22×C4×C29 | SD16 | semidirect |
| 100. #9964 | C29 | direct (N × H) |
| 147. C2×#448 | C2×C29 | semidirect |
| 149. C2×#327 | C2×C29 | semidirect |
| 150. #1446 | C2×C29 | semidirect |
| 151. #1280 | C2×C29 | semidirect |
| 206. C22×Q8 | D4×C29 | semidirect |
| 229. C22⋊C8 | D4×C29 | semidirect |
| 233. C29 | #9964 | direct (N × H) |
| 269. C22×C4 | SD16×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#448 | 2 |
| C29×#2656 | 2 |
| C2×C29×#327 | 2 |
| C29×#1446 | 2 |
| C29×#1280 | 2 |
| #9964 | 29 |