Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
740 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 95 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. #23764536 | C2 | semidirect |
| 2. #23764482 | C2 | semidirect |
| 3. #23761221 | C2 | semidirect |
| 4. #23761221 | C2 | semidirect |
| 7. C2×#14579161 | C22 | semidirect |
| 11. #19098318 | C22 | semidirect |
| 12. #19098318 | C22 | semidirect |
| 82. C2×D4×C79 | SD16 | semidirect |
| 182. C79 | #7750 | semidirect |
| 249. C2×D4 | #11929612 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764536 | 2 |
| #23764482 | 2 |
| #23761221 | 2 |
| C79×#2679 | 2 |
| #7750 | 79 |