Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
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×C79 | #1781 |
| commutator | C22×C4 | C22×C4×C79 |
| Frattini, cosocle | C22×D4 | C23×C79 |
| prime radical | C79×#3484 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C79 ◁ C23×C79 ◁ C23×D4×C79 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C79×#2127 | C2 | semidirect |
| 3. C79×#1781 | C2 | semidirect |
| 4. C2×H(5,𝔽2)×C79 | C4 | semidirect |
| 10. #525×C79 | C4 | semidirect |
| 12. #518×C79 | C4 | semidirect |
| 14. C2×#99×C79 | C22 | semidirect |
| 62. C2×Q8×C79 | C22⋊C4 | semidirect |
| 78. C2×D4×C79 | C22⋊C4 | semidirect |
| 98. C42×C79 | C22⋊C4 | semidirect |
| 167. #12707 | C79 | direct (N × H) |
| 176. #2127 | C2×C79 | semidirect |
| 177. #1781 | C2×C79 | semidirect |
| 178. C79 | #12707 | direct (N × H) |
| 179. C2×H(5,𝔽2) | C4×C79 | semidirect |
| 185. #525 | C4×C79 | semidirect |
| 187. #518 | C4×C79 | semidirect |
| 189. C2×#99 | C22×C79 | semidirect |
| 237. C2×Q8 | C22⋊C4×C79 | semidirect |
| 253. C2×D4 | C22⋊C4×C79 | semidirect |
| 273. C42 | C22⋊C4×C79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C79×#3484 | 2 |
| C79×#2127 | 2 |
| C79×#1781 | 2 |
| #12707 | 79 |