Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
950 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 950 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 |
|---|---|---|
| 1. #23774320 | C2 | semidirect |
| 2. #23774318 | C2 | semidirect |
| 3. #23771794 | C2 | semidirect |
| 4. #23764227 | C2 | semidirect |
| 5. #23762069 | C2 | semidirect |
| 6. #23761232 | C2 | semidirect |
| 7. C79×#1545 | C2 | semidirect |
| 36. #14579161 | D4 | semidirect |
| 41. #14579158 | D4 | semidirect |
| 54. C4⋊(C79⋊C8) | D4 | semidirect |
| 71. C4⋊C8×C79 | D4 | semidirect |
| 107. C4×Dic79 | D8 | semidirect |
| 215. #1545 | D79 | semidirect |
| 217. C79 | #10280 | semidirect |
| 276. C4⋊C8 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774320 | 2 |
| #23774318 | 2 |
| #23771794 | 2 |
| #23764227 | 2 |
| #23762069 | 2 |
| #23761232 | 2 |
| C79×#1545 | 2 |
| #10280 | 79 |