Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
422 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 422 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. #23764141 | C2 | semidirect |
| 5. #23761505 | C2 | semidirect |
| 6. #23761483 | C2 | semidirect |
| 7. C79×#2159 | C2 | semidirect |
| 19. #19098374 | C4 | semidirect |
| 52. #14579093 | C2×C4 | semidirect |
| 64. M32×C79 | C2×C4 | semidirect |
| 85. Dic316 | C4⋊C4 | semidirect |
| 89. D632 | C4⋊C4 | semidirect |
| 183. #2159 | D79 | semidirect |
| 189. C79 | #12943 | semidirect |
| 236. M32 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772200 | 2 |
| C2×#19098374 | 2 |
| #23765110 | 2 |
| #23764141 | 2 |
| #23761505 | 2 |
| #23761483 | 2 |
| C79×#2159 | 2 |
| #12943 | 79 |