Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
850 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 850 conjugacy classes of subgroups — too many to draw. Only its 222 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 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C29 |
| prime radical | C22×D4×C29 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#3236 | C2 | semidirect |
| 4. C29×#1664 | C2 | semidirect |
| 6. C29×#1528 | C2 | semidirect |
| 17. C29×#501 | C22 | semidirect |
| 18. C29×#491 | C22 | semidirect |
| 28. C29×#330 | C22 | semidirect |
| 118. #18999 | C29 | direct (N × H) |
| 146. #3236 | C2×C29 | semidirect |
| 148. #1664 | C2×C29 | semidirect |
| 150. #1528 | C2×C29 | semidirect |
| 175. #501 | C22×C29 | semidirect |
| 176. #491 | C22×C29 | semidirect |
| 186. #330 | C22×C29 | semidirect |
| 238. C29 | #18999 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#563 | 2 |
| C29×#3236 | 2 |
| C29×#3140 | 2 |
| C29×#1664 | 2 |
| C29×#1533 | 2 |
| C29×#1528 | 2 |
| #18999 | 29 |