Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
162 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C29 | D8 |
| commutator | C8 | C2×C16×C29 |
| Frattini, cosocle | C82 | C22×C29 |
| socle | C22×C29 | D4⋊C8 |
| prime radical | C2×D8×C29 | C8 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C29 ◁ C4×C8×C29 ◁ C82×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#1370 | C2 | semidirect |
| 3. C8×C16×C29 | C2 | semidirect |
| 26. D8×C29 | C16 | semidirect |
| 40. #7068 | C29 | direct (N × H) |
| 59. #1370 | C2×C29 | semidirect |
| 60. C8×C16 | C2×C29 | semidirect |
| 94. C29 | #7068 | direct (N × H) |
| 98. D8 | C16×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×D8×C29 | 2 |
| C29×#1370 | 2 |
| C8×C16×C29 | 2 |
| #7068 | 29 |