Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
850 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 850 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 |
| 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×#3192 | C2 | semidirect |
| 2. C29×#3006 | C2 | semidirect |
| 3. C29×#2615 | C2 | semidirect |
| 4. C29×#1964 | C2 | semidirect |
| 5. C29×#1789 | C2 | semidirect |
| 6. C29×#1507 | C2 | semidirect |
| 7. C29×#1305 | C2 | semidirect |
| 45. C22×D4×C29 | D4 | semidirect |
| 53. C2×M16×C29 | D4 | semidirect |
| 65. C2×C4⋊C4×C29 | D4 | semidirect |
| 83. C29×C22⋊C8 | D4 | semidirect |
| 163. #9930 | C29 | direct (N × H) |
| 234. #3192 | C2×C29 | semidirect |
| 235. #3006 | C2×C29 | semidirect |
| 236. #2615 | C2×C29 | semidirect |
| 237. #1964 | C2×C29 | semidirect |
| 238. #1789 | C2×C29 | semidirect |
| 239. #1507 | C2×C29 | semidirect |
| 240. #1305 | C2×C29 | semidirect |
| 326. C22×D4 | D4×C29 | semidirect |
| 334. C2×M16 | D4×C29 | semidirect |
| 346. C2×C4⋊C4 | D4×C29 | semidirect |
| 364. C22⋊C8 | D4×C29 | semidirect |
| 368. C29 | #9930 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3192 | 2 |
| C29×#3006 | 2 |
| C29×#2615 | 2 |
| C29×#1964 | 2 |
| C29×#1789 | 2 |
| C29×#1507 | 2 |
| C29×#1305 | 2 |
| #9930 | 29 |