Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
1386 conjugacy classes of subgroups; only the 366 normal subgroups are shown.
This group has 1386 conjugacy classes of subgroups — too many to draw. Only its 366 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 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C29 |
| prime radical | C29×#2867 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C29 ◁ C43×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C29×#460 | C2 | semidirect |
| 3. C42×Q8×C29 | C2 | semidirect |
| 4. C29×#1982 | C2 | semidirect |
| 5. C29×#1842 | C2 | semidirect |
| 29. C4×Q8×C29 | D4 | semidirect |
| 63. C42×C29 | SD16 | semidirect |
| 66. #33161 | C29 | direct (N × H) |
| 72. Q8×C29 | #127 | semidirect |
| 88. C2×#460 | C2×C29 | semidirect |
| 90. C42×Q8 | C2×C29 | semidirect |
| 91. #1982 | C2×C29 | semidirect |
| 92. #1842 | C2×C29 | semidirect |
| 102. C4×C29 | #460 | semidirect |
| 132. C4×Q8 | D4×C29 | semidirect |
| 143. C29 | #33161 | direct (N × H) |
| 167. C42 | SD16×C29 | semidirect |
| 175. Q8 | C29×#127 | semidirect |
| 200. C4 | C29×#460 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#460 | 2 |
| C29×#2867 | 2 |
| C42×Q8×C29 | 2 |
| C29×#1982 | 2 |
| C29×#1842 | 2 |
| #33161 | 29 |