Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
690 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 111 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. #23772429 | C2 | semidirect |
| 2. #23762114 | C2 | semidirect |
| 3. #23761741 | C2 | semidirect |
| 4. #23761256 | C2 | semidirect |
| 26. C4⋊(C79⋊C8) | D4 | semidirect |
| 192. C79 | #9457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772429 | 2 |
| #23762114 | 2 |
| #23761741 | 2 |
| #23761256 | 2 |
| C79×#2541 | 2 |
| #9457 | 79 |