Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
340 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #23761575 | C2 | direct (N × H) |
| 11. C2×#125×C79 | C4 | semidirect |
| 15. #488×C79 | C4 | semidirect |
| 19. C2×C4×C8×C79 | C4 | semidirect |
| 31. #125×C79 | C2×C4 | semidirect |
| 46. C4×C8×C79 | C2×C4 | semidirect |
| 134. C2×C79 | #1414 | semidirect |
| 140. C79 | C2×#1414 | semidirect |
| 141. C2×#125 | Dic79 | semidirect |
| 145. #488 | Dic79 | semidirect |
| 151. C2×C4×C8 | Dic79 | semidirect |
| 162. #125 | C2×Dic79 | semidirect |
| 182. C4×C8 | C2×Dic79 | semidirect |
| 269. C2 | #23761575 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098360 | 2 |
| C2×#19098358 | 2 |
| #23761575 | 2 |
| C2×#488×C79 | 2 |
| C2×#1414 | 79 |