Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
368 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 71 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. #23765653 | C2 | semidirect |
| 3. #23765450 | C2 | semidirect |
| 5. #23761448 | C2 | semidirect |
| 7. C79×#1332 | C2 | semidirect |
| 106. D316 | Q32 | semidirect |
| 144. #1332 | D79 | semidirect |
| 146. C79 | #12322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×D316 | 2 |
| #23765653 | 2 |
| #23765450 | 2 |
| #23762766 | 2 |
| #23761448 | 2 |
| #23761356 | 2 |
| C79×#1332 | 2 |
| #12322 | 79 |