Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
254 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C29 | C2×D8 |
| commutator | C8 | C22×C8×C29 |
| Frattini, cosocle | C4×C8 | C23×C29 |
| socle | C22×C29 | C4×D8 |
| prime radical | C2×C29×D16 | C4 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C29 ◁ C4×C8×C29 ◁ C82×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C8×D8×C29 | C2 | semidirect |
| 3. C29×#1372 | C2 | semidirect |
| 4. C29×#1331 | C2 | semidirect |
| 5. C29×#1311 | C2 | semidirect |
| 19. C29×D16 | C8 | semidirect |
| 33. D8×C29 | C2×C8 | semidirect |
| 45. C16×C29 | C2×C8 | semidirect |
| 46. #12045 | C29 | direct (N × H) |
| 63. C8×D8 | C2×C29 | semidirect |
| 64. #1372 | C2×C29 | semidirect |
| 65. #1331 | C2×C29 | semidirect |
| 66. #1311 | C2×C29 | semidirect |
| 93. D16 | C8×C29 | semidirect |
| 104. C29 | #12045 | direct (N × H) |
| 108. D8 | C2×C8×C29 | semidirect |
| 120. C16 | C2×C8×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C29×D16 | 2 |
| C8×D8×C29 | 2 |
| C29×#1372 | 2 |
| C29×#1331 | 2 |
| C29×#1311 | 2 |
| #12045 | 29 |