Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
246 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 106 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 | #442 |
| commutator | C8 | C22×C8×C29 |
| Frattini, cosocle | C4×C8 | C23×C29 |
| prime radical | C2×C29×D16 | C4 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C42×C29 ◁ C29×#322 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#1580 | C2 | semidirect |
| 3. C29×#1368 | C2 | semidirect |
| 4. C29×#1333 | C2 | semidirect |
| 5. C29×#1313 | C2 | semidirect |
| 19. C29×D16 | C8 | semidirect |
| 32. D8×C29 | C2×C8 | semidirect |
| 43. C16×C29 | C2×C8 | semidirect |
| 44. #12067 | C29 | direct (N × H) |
| 59. #1580 | C2×C29 | semidirect |
| 60. #1368 | C2×C29 | semidirect |
| 61. #1333 | C2×C29 | semidirect |
| 62. #1313 | C2×C29 | semidirect |
| 87. D16 | C8×C29 | semidirect |
| 97. C29 | #12067 | direct (N × H) |
| 101. D8 | C2×C8×C29 | semidirect |
| 112. C16 | C2×C8×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2177 | 2 |
| C29×#1580 | 2 |
| C29×#1368 | 2 |
| C29×#1333 | 2 |
| C29×#1313 | 2 |
| #12067 | 29 |