Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
558 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 109 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. #23772119 | C2 | semidirect |
| 3. #23762068 | C2 | semidirect |
| 4. #23761959 | C2 | semidirect |
| 5. #23761258 | C2 | semidirect |
| 6. #23761231 | C2 | semidirect |
| 7. C79×#1961 | C2 | semidirect |
| 10. #19098939 | C4 | semidirect |
| 11. #19098909 | C4 | semidirect |
| 112. C2×C8×C79 | D8 | semidirect |
| 198. #1961 | D79 | semidirect |
| 203. C79 | #9293 | semidirect |
| 304. C2×C8 | #11929609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774318 | 2 |
| #23772119 | 2 |
| #23762068 | 2 |
| #23761959 | 2 |
| #23761258 | 2 |
| #23761231 | 2 |
| C79×#1961 | 2 |
| #9293 | 79 |