Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
568 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 95 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. #23776536 | C2 | semidirect |
| 2. #23772981 | C2 | semidirect |
| 3. #23765137 | C2 | semidirect |
| 4. #23761502 | C2 | semidirect |
| 5. C79×#2112 | C2 | semidirect |
| 26. C2×Dic316 | D4 | semidirect |
| 28. C2×D632 | D4 | semidirect |
| 39. #14579093 | D4 | semidirect |
| 52. C2×C16×C79 | D4 | semidirect |
| 146. #2112 | D79 | semidirect |
| 148. C79 | #13309 | semidirect |
| 191. C2×C16 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776536 | 2 |
| #23772981 | 2 |
| #23765137 | 2 |
| #23761502 | 2 |
| C79×#2112 | 2 |
| #13309 | 79 |