Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
780 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C29 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C29 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C29 ◁ C2×C42×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C29×#496 | C2 | semidirect |
| 2. C29×#2819 | C2 | semidirect |
| 3. C29×#1961 | C2 | semidirect |
| 4. C2×C29×#329 | C2 | semidirect |
| 5. C29×#1295 | C2 | semidirect |
| 33. C29×#127 | D4 | semidirect |
| 46. C29×#97 | D4 | semidirect |
| 87. #10078 | C29 | direct (N × H) |
| 121. C2×#496 | C2×C29 | semidirect |
| 122. #2819 | C2×C29 | semidirect |
| 123. #1961 | C2×C29 | semidirect |
| 124. C2×#329 | C2×C29 | semidirect |
| 125. #1295 | C2×C29 | semidirect |
| 178. #127 | D4×C29 | semidirect |
| 191. #97 | D4×C29 | semidirect |
| 194. C29 | #10078 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#496 | 2 |
| C29×#2819 | 2 |
| C29×#1961 | 2 |
| C2×C29×#329 | 2 |
| C29×#1295 | 2 |
| #10078 | 29 |