Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
212 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 212 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. #23765238 | C2 | semidirect |
| 3. #23761475 | C2 | semidirect |
| 4. #23761373 | C2 | semidirect |
| 5. #23761372 | C2 | semidirect |
| 6. #23761316 | C2 | semidirect |
| 7. C79×#2170 | C2 | semidirect |
| 25. #14579107 | C8 | semidirect |
| 26. #14579105 | C8 | semidirect |
| 27. #14579104 | C8 | semidirect |
| 28. #14579102 | C8 | semidirect |
| 105. #2170 | D79 | semidirect |
| 110. C79 | #12047 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765279 | 2 |
| #23765238 | 2 |
| #23761475 | 2 |
| #23761373 | 2 |
| #23761372 | 2 |
| #23761316 | 2 |
| C79×#2170 | 2 |
| #12047 | 79 |