Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
424 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 73 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. #23765625 | C2 | semidirect |
| 3. #23765534 | C2 | semidirect |
| 4. #23761445 | C2 | semidirect |
| 5. #23761360 | C2 | semidirect |
| 6. D4⋊(C79⋊C16) | C2 | semidirect |
| 7. C79×#1673 | C2 | semidirect |
| 16. C4⋊(C79⋊C16) | C22 | semidirect |
| 19. C4×C79⋊C16 | C22 | semidirect |
| 20. #500×C79 | C22 | semidirect |
| 23. #335×C79 | C22 | semidirect |
| 71. D632 | SD16 | semidirect |
| 155. #1673 | D79 | semidirect |
| 159. C79 | #12368 | semidirect |
| 162. #500 | C2×D79 | semidirect |
| 175. #335 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D632 | 2 |
| #23765625 | 2 |
| #23765534 | 2 |
| #23761445 | 2 |
| #23761360 | 2 |
| D4⋊(C79⋊C16) | 2 |
| C79×#1673 | 2 |
| #12368 | 79 |