Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
634 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 634 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. #23774707 | C2 | semidirect |
| 2. #23772864 | C2 | semidirect |
| 3. #23764195 | C2 | semidirect |
| 4. #23761851 | C2 | semidirect |
| 5. #23761850 | C2 | semidirect |
| 6. #23761274 | C2 | semidirect |
| 7. C79×#3036 | C2 | semidirect |
| 127. C2×D4×C79 | D8 | semidirect |
| 251. #3036 | D79 | semidirect |
| 256. C79 | #10254 | semidirect |
| 360. C2×D4 | #11929609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774707 | 2 |
| #23772864 | 2 |
| #23764195 | 2 |
| #23761851 | 2 |
| #23761850 | 2 |
| #23761274 | 2 |
| C79×#3036 | 2 |
| #10254 | 79 |