Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
1216 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 1216 conjugacy classes of subgroups — too many to draw. Only its 146 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C29 | #1781 |
| commutator | C22×C4 | C22×C4×C29 |
| Frattini, cosocle | C22×D4 | C23×C29 |
| prime radical | C29×#3484 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C29 ◁ C23×C29 ◁ C23×D4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#2127 | C2 | semidirect |
| 3. C29×#1781 | C2 | semidirect |
| 4. C2×C29×H(5,𝔽2) | C4 | semidirect |
| 10. C29×#525 | C4 | semidirect |
| 12. C29×#518 | C4 | semidirect |
| 14. C2×C29×#99 | C22 | semidirect |
| 62. C2×Q8×C29 | C22⋊C4 | semidirect |
| 78. C2×D4×C29 | C22⋊C4 | semidirect |
| 98. C42×C29 | C22⋊C4 | semidirect |
| 99. #12707 | C29 | direct (N × H) |
| 144. #2127 | C2×C29 | semidirect |
| 145. #1781 | C2×C29 | semidirect |
| 171. C2×H(5,𝔽2) | C4×C29 | semidirect |
| 177. #525 | C4×C29 | semidirect |
| 179. #518 | C4×C29 | semidirect |
| 181. C2×#99 | C22×C29 | semidirect |
| 226. C29 | #12707 | direct (N × H) |
| 237. C2×Q8 | C22⋊C4×C29 | semidirect |
| 253. C2×D4 | C22⋊C4×C29 | semidirect |
| 273. C42 | C22⋊C4×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3484 | 2 |
| C29×#2127 | 2 |
| C29×#1781 | 2 |
| #12707 | 29 |