Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
508 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 4. #23761279 | C2 | semidirect |
| 5. #23761267 | C2 | semidirect |
| 6. #23761248 | C2 | semidirect |
| 7. C79×#2549 | C2 | semidirect |
| 27. C22×D316 | Q8 | semidirect |
| 36. C2×C4⋊Dic79 | Q8 | semidirect |
| 230. #2549 | D79 | semidirect |
| 237. C79 | #10374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764236 | 2 |
| #23761967 | 2 |
| C2×#19098296 | 2 |
| #23761279 | 2 |
| #23761267 | 2 |
| #23761248 | 2 |
| C79×#2549 | 2 |
| #10374 | 79 |