Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
284 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 110 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 | #493 |
| commutator, Frattini, cosocle | C4×C8 | C23×C29 |
| prime radical | C29×#493 | C22 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C42×C29 ◁ C82×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C29×#2254 | C2 | semidirect |
| 3. C29×#2241 | C2 | semidirect |
| 5. C29×#1707 | C2 | semidirect |
| 7. C8×C16×C29 | C2 | semidirect |
| 68. C16×C29 | SD16 | semidirect |
| 69. #12505 | C29 | direct (N × H) |
| 86. C8×C29 | SD32 | semidirect |
| 89. #2254 | C2×C29 | semidirect |
| 91. #2241 | C2×C29 | semidirect |
| 93. #1707 | C2×C29 | semidirect |
| 95. C8×C16 | C2×C29 | semidirect |
| 148. C29 | #12505 | direct (N × H) |
| 172. C16 | SD16×C29 | semidirect |
| 189. C8 | C29×SD32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2254 | 2 |
| C29×#2248 | 2 |
| C29×#2241 | 2 |
| C29×#2240 | 2 |
| C29×#1707 | 2 |
| C29×#1706 | 2 |
| C8×C16×C29 | 2 |
| #12505 | 29 |