Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
234 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 74 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 | #327 |
| commutator | C2×C8 | C2×C8×C29 |
| Frattini, cosocle | C2×#97 | C22×C29 |
| prime radical | C23×C29 | #102 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C22×C4×C29 ◁ C2×C29×#97 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 15. C2×Q16×C29 | C8 | semidirect |
| 59. #7111 | C29 | direct (N × H) |
| 118. C2×Q16 | C8×C29 | semidirect |
| 135. C29 | #7111 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#1971 | 2 |
| C29×#1377 | 2 |
| C29×#1275 | 2 |
| #7111 | 29 |