Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
408 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 2. C2×#19098385 | C2 | semidirect |
| 4. #23764136 | C2 | semidirect |
| 5. #23761509 | C2 | semidirect |
| 6. #23761479 | C2 | semidirect |
| 18. #19098367 | C4 | semidirect |
| 19. #19098364 | C4 | semidirect |
| 87. Q16×C79 | C4⋊C4 | semidirect |
| 91. D8×C79 | C4⋊C4 | semidirect |
| 163. C79 | #12955 | semidirect |
| 229. Q16 | Dic79⋊C4 | semidirect |
| 233. D8 | Dic79⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098685 | 2 |
| C2×#19098385 | 2 |
| #23765112 | 2 |
| #23764136 | 2 |
| #23761509 | 2 |
| #23761479 | 2 |
| C2×#360×C79 | 2 |
| #12955 | 79 |