Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
330 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 330 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. #23765627 | C2 | semidirect |
| 3. #23765442 | C2 | semidirect |
| 4. #23761456 | C2 | semidirect |
| 5. #23761360 | C2 | semidirect |
| 6. D4⋊(C79⋊C16) | C2 | semidirect |
| 7. C79×#1669 | C2 | semidirect |
| 92. D4×C79 | SD32 | semidirect |
| 140. #1669 | D79 | semidirect |
| 144. C79 | #12344 | semidirect |
| 234. D4 | #14579104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23775748 | 2 |
| #23765627 | 2 |
| #23765442 | 2 |
| #23761456 | 2 |
| #23761360 | 2 |
| D4⋊(C79⋊C16) | 2 |
| C79×#1669 | 2 |
| #12344 | 79 |