Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
490 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 109 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. #23762085 | C2 | semidirect |
| 5. #23761258 | C2 | semidirect |
| 6. #23761231 | C2 | semidirect |
| 7. C79×#1993 | C2 | semidirect |
| 10. #19098937 | C4 | semidirect |
| 11. #19098913 | C4 | semidirect |
| 101. C2×C8×C79 | SD16 | semidirect |
| 177. #1993 | D79 | semidirect |
| 182. C79 | #9289 | semidirect |
| 272. C2×C8 | #11929611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774325 | 2 |
| #23772119 | 2 |
| #23762085 | 2 |
| #23761959 | 2 |
| #23761258 | 2 |
| #23761231 | 2 |
| C79×#1993 | 2 |
| #9289 | 79 |