Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
768 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 147 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 |
|---|---|---|
| 3. #23761521 | C2 | semidirect |
| 4. #23761520 | C2 | semidirect |
| 5. C79×#1391 | C2 | semidirect |
| 7. C22×#11929607 | C4 | semidirect |
| 8. C2×M16×D79 | C4 | semidirect |
| 13. #19098535 | C4 | semidirect |
| 15. #99×D79 | C4 | semidirect |
| 16. #19098531 | C4 | semidirect |
| 18. #19098529 | C4 | semidirect |
| 35. C2×#11929608 | C2×C4 | semidirect |
| 41. C22×C79⋊C8 | C2×C4 | semidirect |
| 51. #14579076 | C2×C4 | semidirect |
| 58. C2×M16×C79 | C2×C4 | semidirect |
| 59. C22×C8×C79 | C2×C4 | semidirect |
| 62. #99×C79 | C2×C4 | semidirect |
| 216. #1391 | D79 | semidirect |
| 217. C79 | #12577 | semidirect |
| 254. C2×M16 | C4×D79 | semidirect |
| 257. C22×C8 | C4×D79 | semidirect |
| 271. #99 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #410×D79 | 2 |
| #23771842 | 2 |
| #23761521 | 2 |
| #23761520 | 2 |
| C79×#1391 | 2 |
| #12577 | 79 |