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. #23761412 | C2 | semidirect |
| 5. #23761410 | C2 | semidirect |
| 6. #23761408 | C2 | semidirect |
| 7. C79×#1348 | C2 | semidirect |
| 8. C2×#14579184 | C4 | semidirect |
| 13. #19098801 | C4 | semidirect |
| 14. #19098800 | C4 | semidirect |
| 18. #19098600 | C4 | semidirect |
| 32. C2×D632 | C2×C4 | semidirect |
| 53. #14579095 | C2×C4 | semidirect |
| 58. C2×Q16×C79 | C2×C4 | semidirect |
| 63. #107×C79 | C2×C4 | semidirect |
| 200. #1348 | D79 | semidirect |
| 203. C79 | #11704 | semidirect |
| 227. C2×Q16 | 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 |
|---|---|
| #23772983 | 2 |
| #23765009 | 2 |
| #340×D79 | 2 |
| #23761412 | 2 |
| #23761410 | 2 |
| #23761408 | 2 |
| C79×#1348 | 2 |
| #11704 | 79 |