Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
698 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 146 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 | C2×D8 |
| commutator, Frattini, cosocle | C22×C8 | C23×C29 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C29 ◁ C2×C42×C29 ◁ C2×C4×C8×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C29×D16 | C2 | semidirect |
| 2. C2×C29×#493 | C2 | semidirect |
| 3. C2×C29×#357 | C2 | semidirect |
| 4. C29×#1970 | C2 | semidirect |
| 5. C29×#1374 | C2 | semidirect |
| 35. C2×D8×C29 | D4 | semidirect |
| 46. C2×C16×C29 | D4 | semidirect |
| 90. #13325 | C29 | direct (N × H) |
| 115. C2×C4×C29 | D16 | semidirect |
| 125. C22×D16 | C2×C29 | semidirect |
| 126. C2×#493 | C2×C29 | semidirect |
| 127. C2×#357 | C2×C29 | semidirect |
| 128. #1970 | C2×C29 | semidirect |
| 129. #1374 | C2×C29 | semidirect |
| 187. C2×D8 | D4×C29 | semidirect |
| 198. C2×C16 | D4×C29 | semidirect |
| 202. C29 | #13325 | direct (N × H) |
| 267. C2×C4 | C29×D16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C29×D16 | 2 |
| C2×C29×#493 | 2 |
| C2×C29×#357 | 2 |
| C29×#1970 | 2 |
| C29×#1374 | 2 |
| #13325 | 29 |