Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
458 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 458 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 |
|---|---|---|
| 1. D4×D632 | C2 | semidirect |
| 2. #23765649 | C2 | semidirect |
| 3. #23765432 | C2 | semidirect |
| 4. #23761445 | C2 | semidirect |
| 5. #23761360 | C2 | semidirect |
| 6. D4⋊(C79⋊C16) | C2 | semidirect |
| 7. C79×#1667 | C2 | semidirect |
| 17. C4⋊(C79⋊C16) | C22 | semidirect |
| 19. C4×C79⋊C16 | C22 | semidirect |
| 20. #493×C79 | C22 | semidirect |
| 23. #335×C79 | C22 | semidirect |
| 73. D632 | D8 | semidirect |
| 110. D4×C79 | D16 | semidirect |
| 166. #1667 | D79 | semidirect |
| 170. C79 | #12316 | semidirect |
| 176. #493 | C2×D79 | semidirect |
| 186. #335 | C2×D79 | semidirect |
| 282. D4 | #14579102 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D632 | 2 |
| #23765649 | 2 |
| #23765432 | 2 |
| #23761445 | 2 |
| #23761360 | 2 |
| D4⋊(C79⋊C16) | 2 |
| C79×#1667 | 2 |
| #12316 | 79 |