Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
504 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. #23764734 | C2 | semidirect |
| 3. #23764541 | C2 | semidirect |
| 5. #23761222 | C2 | semidirect |
| 7. C79×#1272 | C2 | semidirect |
| 108. C2×Q8×C79 | SD16 | semidirect |
| 211. #1272 | D79 | semidirect |
| 214. C79 | #7753 | semidirect |
| 280. C2×Q8 | #11929613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23770418 | 2 |
| #23764734 | 2 |
| #23764541 | 2 |
| #23764485 | 2 |
| #23761222 | 2 |
| #23761220 | 2 |
| C79×#1272 | 2 |
| #7753 | 79 |