Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
376 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 105 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. C4×C4⋊(C79⋊C8) | C2 | semidirect |
| 3. #23762175 | C2 | semidirect |
| 6. #23761296 | C2 | semidirect |
| 7. C79×#1276 | C2 | semidirect |
| 17. #19098308 | C4 | semidirect |
| 18. #19098306 | C4 | semidirect |
| 162. #1276 | D79 | semidirect |
| 163. C79 | #9577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764228 | 2 |
| C4×C4⋊(C79⋊C8) | 2 |
| #23762175 | 2 |
| #23762047 | 2 |
| #23761800 | 2 |
| #23761296 | 2 |
| C79×#1276 | 2 |
| #9577 | 79 |