Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
408 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 4. #23764136 | C2 | semidirect |
| 5. #23761510 | C2 | semidirect |
| 6. #23761479 | C2 | semidirect |
| 7. C2×#365×C79 | C2 | semidirect |
| 18. #19098368 | C4 | semidirect |
| 19. #19098365 | C4 | semidirect |
| 71. Dic316 | C4⋊C4 | semidirect |
| 75. D632 | C4⋊C4 | semidirect |
| 157. C2×#365 | D79 | semidirect |
| 163. C79 | #12955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098684 | 2 |
| C2×#19098372 | 2 |
| #23765113 | 2 |
| #23764136 | 2 |
| #23761510 | 2 |
| #23761479 | 2 |
| C2×#365×C79 | 2 |
| #12955 | 79 |