Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
290 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 79 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. M64×D79 | C2 | semidirect |
| 3. #368×D79 | C2 | semidirect |
| 4. #23761594 | C2 | semidirect |
| 5. #23761592 | C2 | semidirect |
| 6. #23761590 | C2 | semidirect |
| 7. C79×#1419 | C2 | semidirect |
| 127. #1419 | D79 | semidirect |
| 128. C79 | #13625 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098992 | 2 |
| M64×D79 | 2 |
| #368×D79 | 2 |
| #23761594 | 2 |
| #23761592 | 2 |
| #23761590 | 2 |
| C79×#1419 | 2 |
| #13625 | 79 |