Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
794 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 105 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. #23774318 | C2 | semidirect |
| 2. #23772864 | C2 | semidirect |
| 3. #23762068 | C2 | semidirect |
| 4. #23761894 | C2 | semidirect |
| 5. #23761791 | C2 | semidirect |
| 6. #23761303 | C2 | semidirect |
| 7. C79×#2541 | C2 | semidirect |
| 38. #14579161 | D4 | semidirect |
| 39. #14579158 | D4 | semidirect |
| 47. C4⋊(C79⋊C8) | D4 | semidirect |
| 48. C4⋊(C79⋊C8) | D4 | semidirect |
| 124. C2×D4×C79 | D8 | semidirect |
| 243. #2541 | D79 | semidirect |
| 248. C79 | #10238 | semidirect |
| 352. C2×D4 | #11929609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774318 | 2 |
| #23772864 | 2 |
| #23762068 | 2 |
| #23761894 | 2 |
| #23761791 | 2 |
| #23761303 | 2 |
| C79×#2541 | 2 |
| #10238 | 79 |