Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
808 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 808 conjugacy classes of subgroups — too many to draw. Only its 102 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 | #392 |
| commutator, Frattini, cosocle | C23×C4 | C23×C29 |
| prime radical | C29×#2615 | C2 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C29×#3193 | C2 | semidirect |
| 2. C29×#3007 | C2 | semidirect |
| 4. C29×#1996 | C2 | semidirect |
| 5. C29×#1789 | C2 | semidirect |
| 6. C29×#1507 | C2 | semidirect |
| 7. C29×#1305 | C2 | semidirect |
| 39. C22×Q8×C29 | D4 | semidirect |
| 52. C2×M16×C29 | D4 | semidirect |
| 65. C2×C4⋊C4×C29 | D4 | semidirect |
| 82. C29×C22⋊C8 | D4 | semidirect |
| 160. #9934 | C29 | direct (N × H) |
| 226. #3193 | C2×C29 | semidirect |
| 227. #3007 | C2×C29 | semidirect |
| 229. #1996 | C2×C29 | semidirect |
| 230. #1789 | C2×C29 | semidirect |
| 231. #1507 | C2×C29 | semidirect |
| 232. #1305 | C2×C29 | semidirect |
| 308. C22×Q8 | D4×C29 | semidirect |
| 321. C2×M16 | D4×C29 | semidirect |
| 334. C2×C4⋊C4 | D4×C29 | semidirect |
| 351. C22⋊C8 | D4×C29 | semidirect |
| 355. C29 | #9934 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3193 | 2 |
| C29×#3007 | 2 |
| C29×#2615 | 2 |
| C29×#1996 | 2 |
| C29×#1789 | 2 |
| C29×#1507 | 2 |
| C29×#1305 | 2 |
| #9934 | 29 |