Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
194 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 59 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. #23765285 | C2 | semidirect |
| 3. #23765276 | C2 | semidirect |
| 4. #23761607 | C2 | semidirect |
| 5. #23761588 | C2 | semidirect |
| 6. #23761535 | C2 | semidirect |
| 7. C79×#1419 | C2 | semidirect |
| 11. #19098401 | C4 | semidirect |
| 12. #19098398 | C4 | semidirect |
| 24. Dic632 | C2×C4 | semidirect |
| 26. D1264 | C2×C4 | semidirect |
| 32. C79⋊C32 | C2×C4 | semidirect |
| 92. #1419 | D79 | semidirect |
| 95. C79 | #13658 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765713 | 2 |
| #23765285 | 2 |
| #23765276 | 2 |
| #23761607 | 2 |
| #23761588 | 2 |
| #23761535 | 2 |
| C79×#1419 | 2 |
| #13658 | 79 |