Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
330 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 67 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. #23765442 | C2 | semidirect |
| 3. #23762762 | C2 | semidirect |
| 4. #23761455 | C2 | semidirect |
| 5. #23761362 | C2 | semidirect |
| 6. #23761356 | C2 | semidirect |
| 7. C79×#2241 | C2 | semidirect |
| 104. D316 | SD32 | semidirect |
| 138. #2241 | D79 | semidirect |
| 144. C79 | #12344 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23775747 | 2 |
| #23765442 | 2 |
| #23762762 | 2 |
| #23761455 | 2 |
| #23761362 | 2 |
| #23761356 | 2 |
| C79×#2241 | 2 |
| #12344 | 79 |