Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
568 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 101 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. #23776534 | C2 | semidirect |
| 2. C2×#19098999 | C2 | semidirect |
| 3. #23765136 | C2 | semidirect |
| 4. #23765116 | C2 | semidirect |
| 5. #23764298 | C2 | semidirect |
| 6. #23761486 | C2 | semidirect |
| 7. C79×#3155 | C2 | semidirect |
| 38. C2×Dic316 | D4 | semidirect |
| 40. C2×D632 | D4 | semidirect |
| 51. #14579101 | D4 | semidirect |
| 53. C2×C79⋊C16 | D4 | semidirect |
| 220. #3155 | D79 | semidirect |
| 225. C79 | #13334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776534 | 2 |
| C2×#19098999 | 2 |
| #23765136 | 2 |
| #23765116 | 2 |
| #23764298 | 2 |
| #23761486 | 2 |
| C79×#3155 | 2 |
| #13334 | 79 |