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. #23765650 | C2 | semidirect |
| 3. #23765436 | C2 | semidirect |
| 4. #23762755 | C2 | semidirect |
| 5. #23761447 | C2 | semidirect |
| 6. #23761362 | C2 | semidirect |
| 7. C79×D4⋊C16 | C2 | semidirect |
| 13. #19098940 | C22 | semidirect |
| 20. #19098316 | C22 | semidirect |
| 23. C4⋊C16×C79 | C22 | semidirect |
| 24. C4×C16×C79 | C22 | semidirect |
| 79. D632 | D8 | semidirect |
| 105. D4×C79 | D16 | semidirect |
| 169. D4⋊C16 | D79 | semidirect |
| 170. C79 | #12316 | semidirect |
| 183. C4⋊C16 | C2×D79 | semidirect |
| 185. C4×C16 | C2×D79 | semidirect |
| 282. D4 | D1264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D632 | 2 |
| #23765650 | 2 |
| #23765436 | 2 |
| #23762755 | 2 |
| #23761447 | 2 |
| #23761362 | 2 |
| C79×D4⋊C16 | 2 |
| #12316 | 79 |