Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
324 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 82 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 | #447 |
| 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 ◁ C8×Q8×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C29×#2209 | C2 | semidirect |
| 4. C29×#1670 | C2 | semidirect |
| 6. C29×Q8⋊C16 | C2 | semidirect |
| 7. C29×#1332 | C2 | semidirect |
| 88. #12333 | C29 | direct (N × H) |
| 117. #2209 | C2×C29 | semidirect |
| 118. #1670 | C2×C29 | semidirect |
| 120. Q8⋊C16 | C2×C29 | semidirect |
| 121. #1332 | C2×C29 | semidirect |
| 186. C29 | #12333 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3396 | 2 |
| C29×#2248 | 2 |
| C29×#2209 | 2 |
| C29×#1670 | 2 |
| C29×#1361 | 2 |
| C29×Q8⋊C16 | 2 |
| C29×#1332 | 2 |
| #12333 | 29 |