Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
406 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 65 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. #23775010 | C2 | semidirect |
| 2. #23765666 | C2 | semidirect |
| 3. #23765435 | C2 | semidirect |
| 4. #23762880 | C2 | semidirect |
| 5. #23761442 | C2 | semidirect |
| 6. #23761359 | C2 | semidirect |
| 7. C79×#1333 | C2 | semidirect |
| 14. #19098940 | C22 | semidirect |
| 21. C4⋊(C79⋊C16) | C22 | semidirect |
| 25. #346×C79 | C22 | semidirect |
| 26. #334×C79 | C22 | semidirect |
| 106. D8×C79 | D8 | semidirect |
| 185. #1333 | D79 | semidirect |
| 187. C79 | #12324 | semidirect |
| 204. #346 | C2×D79 | semidirect |
| 205. #334 | C2×D79 | semidirect |
| 275. D8 | D632 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23775010 | 2 |
| #23765666 | 2 |
| #23765435 | 2 |
| #23762880 | 2 |
| #23761442 | 2 |
| #23761359 | 2 |
| C79×#1333 | 2 |
| #12324 | 79 |