Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
580 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 107 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. #23763467 | C2 | semidirect |
| 3. #336×D79 | C2 | semidirect |
| 4. #23761224 | C2 | semidirect |
| 5. #23761222 | C2 | semidirect |
| 6. #23761221 | C2 | semidirect |
| 7. C79×#1270 | C2 | semidirect |
| 231. #1270 | D79 | semidirect |
| 232. C79 | #7654 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771730 | 2 |
| #23763467 | 2 |
| #336×D79 | 2 |
| #23761224 | 2 |
| #23761222 | 2 |
| #23761221 | 2 |
| C79×#1270 | 2 |
| #7654 | 79 |