Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
994 conjugacy classes of subgroups; only the 382 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 382 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 | #127 |
| commutator, Frattini, cosocle | C42 | C24×C29 |
| prime radical | C2×C29×#127 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C29 ◁ C2×C42×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C29×#498 | C2 | semidirect |
| 3. C29×#1705 | C2 | direct (N × H) |
| 4. C2×C82×C29 | C2 | semidirect |
| 9. C29×#498 | C22 | semidirect |
| 14. C82×C29 | C22 | semidirect |
| 40. C2×C8×C29 | SD16 | semidirect |
| 46. C2×#1705 | C29 | direct (N × H) |
| 59. C8×C29 | C2×SD16 | semidirect |
| 60. C2×#498 | C2×C29 | semidirect |
| 62. #1705 | C2×C29 | direct (N × H) |
| 63. C2×C82 | C2×C29 | semidirect |
| 75. #498 | C22×C29 | semidirect |
| 80. C82 | C22×C29 | semidirect |
| 82. C2×C29 | #1705 | direct (N × H) |
| 99. C29 | C2×#1705 | direct (N × H) |
| 110. C2×C8 | SD16×C29 | semidirect |
| 128. C8 | C2×SD16×C29 | semidirect |
| 137. C2 | C29×#1705 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#498 | 2 |
| C2×C29×#492 | 2 |
| C29×#1705 | 2 |
| C2×C82×C29 | 2 |
| C2×#1705 | 29 |