Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
580 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 103 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. #23763683 | C2 | semidirect |
| 4. #23761517 | C2 | semidirect |
| 19. #353×C79 | C4 | semidirect |
| 47. #99×C79 | C2×C4 | semidirect |
| 79. C2×D4×C79 | C4⋊C4 | semidirect |
| 89. C42×C79 | C4⋊C4 | semidirect |
| 167. C79 | #12966 | semidirect |
| 179. #353 | Dic79 | semidirect |
| 204. #99 | C2×Dic79 | semidirect |
| 221. C2×D4 | C4⋊Dic79 | semidirect |
| 251. C42 | C4⋊Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766577 | 2 |
| #23763799 | 2 |
| #23763683 | 2 |
| #23761517 | 2 |
| C2×#353×C79 | 2 |
| #12966 | 79 |