Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
552 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 83 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. #23763137 | C2 | semidirect |
| 3. #23761713 | C2 | semidirect |
| 4. #23761404 | C2 | semidirect |
| 5. #23761403 | C2 | semidirect |
| 6. #23761402 | C2 | semidirect |
| 7. C79×#1345 | C2 | semidirect |
| 232. #1345 | D79 | semidirect |
| 233. C79 | #11699 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23769152 | 2 |
| #23763137 | 2 |
| #23761713 | 2 |
| #23761404 | 2 |
| #23761403 | 2 |
| #23761402 | 2 |
| C79×#1345 | 2 |
| #11699 | 79 |