Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
504 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23765009 | C2 | semidirect |
| 3. #340×D79 | C2 | semidirect |
| 4. #23761413 | C2 | semidirect |
| 5. #23761411 | C2 | semidirect |
| 6. #23761409 | C2 | semidirect |
| 7. C79×#1347 | C2 | semidirect |
| 8. C2×#14579180 | C4 | semidirect |
| 13. #19098805 | C4 | semidirect |
| 15. #19098796 | C4 | semidirect |
| 18. #19098600 | C4 | semidirect |
| 31. C2×Dic316 | C2×C4 | semidirect |
| 53. #14579095 | C2×C4 | semidirect |
| 58. C2×D8×C79 | C2×C4 | semidirect |
| 63. #107×C79 | C2×C4 | semidirect |
| 202. #1347 | D79 | semidirect |
| 203. C79 | #11704 | semidirect |
| 229. C2×D8 | C4×D79 | semidirect |
| 255. #107 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772979 | 2 |
| #23765009 | 2 |
| #340×D79 | 2 |
| #23761413 | 2 |
| #23761411 | 2 |
| #23761409 | 2 |
| C79×#1347 | 2 |
| #11704 | 79 |