Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
186 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C29×C32 | D4 |
| commutator | C4 | C22×C16×C29 |
| Frattini, cosocle | C2×C16 | C23×C29 |
| socle | C2×C29 | D4×C16 |
| prime radical | C29×#135 | C8 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C29×C32 ◁ C2×C29×C32 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C29×#2258 | C2 | semidirect |
| 3. C29×#1422 | C2 | semidirect |
| 4. C29×#1401 | C2 | semidirect |
| 5. C4×C29×C32 | C2 | semidirect |
| 44. #13647 | C29 | direct (N × H) |
| 56. #2258 | C2×C29 | semidirect |
| 58. #1422 | C2×C29 | semidirect |
| 59. #1401 | C2×C29 | semidirect |
| 60. C4×C32 | C2×C29 | semidirect |
| 94. C29 | #13647 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2258 | 2 |
| C29×#2170 | 2 |
| C29×#1422 | 2 |
| C29×#1401 | 2 |
| C4×C29×C32 | 2 |
| #13647 | 29 |