Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
250 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 1. C2×#19098400 | C2 | semidirect |
| 3. C4×C79⋊C32 | C2 | semidirect |
| 4. C79×#2247 | C2 | semidirect |
| 19. C79⋊C32 | D4 | semidirect |
| 59. C4×C79 | SD64 | semidirect |
| 67. #2247 | D79 | semidirect |
| 70. C79 | #13727 | semidirect |
| 125. C4 | #19098400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098400 | 2 |
| #23765650 | 2 |
| C4×C79⋊C32 | 2 |
| C79×#2247 | 2 |
| #13727 | 79 |