Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
360 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 87 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. #23765656 | C2 | semidirect |
| 2. #23765655 | C2 | semidirect |
| 3. #23765649 | C2 | semidirect |
| 4. #23763014 | C2 | semidirect |
| 5. #23763005 | C2 | semidirect |
| 6. #23761316 | C2 | semidirect |
| 7. C79×#2246 | C2 | semidirect |
| 53. C79⋊C16 | D8 | semidirect |
| 65. C16×C79 | D8 | semidirect |
| 106. #2246 | D79 | semidirect |
| 110. C79 | #12519 | semidirect |
| 168. C16 | #11929609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765656 | 2 |
| #23765655 | 2 |
| #23765649 | 2 |
| #23763014 | 2 |
| #23763005 | 2 |
| #23761316 | 2 |
| C79×#2246 | 2 |
| #12519 | 79 |