Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
498 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 498 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 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×C22⋊C4 | C23×C29 |
| prime radical | C29×#1595 | C2 |
| LCS | G ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C23×C29 ◁ C2×C22⋊C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C29×#2693 | C2 | semidirect |
| 2. C29×#2044 | C2 | semidirect |
| 3. C29×#1607 | C2 | semidirect |
| 5. C29×#1344 | C2 | semidirect |
| 6. C29×#1343 | C2 | semidirect |
| 7. C29×#1326 | C2 | semidirect |
| 118. C22⋊C4×C29 | D8 | semidirect |
| 119. #12149 | C29 | direct (N × H) |
| 179. #2693 | C2×C29 | semidirect |
| 180. #2044 | C2×C29 | semidirect |
| 181. #1607 | C2×C29 | semidirect |
| 183. #1344 | C2×C29 | semidirect |
| 184. #1343 | C2×C29 | semidirect |
| 185. #1326 | C2×C29 | semidirect |
| 285. C29 | #12149 | direct (N × H) |
| 339. C22⋊C4 | D8×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2693 | 2 |
| C29×#2044 | 2 |
| C29×#1607 | 2 |
| C29×#1595 | 2 |
| C29×#1344 | 2 |
| C29×#1343 | 2 |
| C29×#1326 | 2 |
| #12149 | 29 |