Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
590 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 214 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×C79 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C79 |
| prime radical | C24×C79 | D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C23×C4×C79 ◁ C23×C8×C79 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C79×#2236 | C2 | semidirect |
| 3. C79×#2216 | C2 | semidirect |
| 4. C79×#2188 | C2 | semidirect |
| 9. C2×Q32×C79 | C22 | semidirect |
| 17. #366×C79 | C22 | semidirect |
| 18. #358×C79 | C22 | semidirect |
| 75. C23×C79 | Q32 | semidirect |
| 111. #33755 | C79 | direct (N × H) |
| 118. #2236 | C2×C79 | semidirect |
| 119. #2216 | C2×C79 | semidirect |
| 120. #2188 | C2×C79 | semidirect |
| 122. C79 | #33755 | direct (N × H) |
| 126. C2×Q32 | C22×C79 | semidirect |
| 134. #366 | C22×C79 | semidirect |
| 135. #358 | C22×C79 | semidirect |
| 192. C23 | Q32×C79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#467×C79 | 2 |
| C79×#2236 | 2 |
| C79×#2216 | 2 |
| C79×#2188 | 2 |
| C2×C22⋊C16×C79 | 2 |
| #33755 | 79 |