Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
302 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 82 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 | #447 |
| commutator, Frattini, cosocle | C4×C8 | C23×C79 |
| prime radical | C79×#3341 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C42×C79 ◁ C8×D4×C79 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C79×#2241 | C2 | semidirect |
| 3. C79×#2208 | C2 | semidirect |
| 4. C79×#1669 | C2 | semidirect |
| 5. C79×#1365 | C2 | semidirect |
| 6. C79×#1331 | C2 | semidirect |
| 7. C79×D4⋊C16 | C2 | semidirect |
| 127. #12347 | C79 | direct (N × H) |
| 134. #2241 | C2×C79 | semidirect |
| 135. #2208 | C2×C79 | semidirect |
| 136. #1669 | C2×C79 | semidirect |
| 137. #1365 | C2×C79 | semidirect |
| 138. #1331 | C2×C79 | semidirect |
| 139. D4⋊C16 | C2×C79 | semidirect |
| 140. C79 | #12347 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C79×#3341 | 2 |
| C79×#2241 | 2 |
| C79×#2208 | 2 |
| C79×#1669 | 2 |
| C79×#1365 | 2 |
| C79×#1331 | 2 |
| C79×D4⋊C16 | 2 |
| #12347 | 79 |