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 |
|---|---|---|
| 2. #23772340 | C2 | semidirect |
| 5. #23761965 | C2 | semidirect |
| 6. #23761259 | C2 | semidirect |
| 7. C79×#1275 | C2 | semidirect |
| 10. #19098936 | C4 | semidirect |
| 11. #19098910 | C4 | semidirect |
| 106. C2×C8×C79 | SD16 | semidirect |
| 183. #1275 | D79 | semidirect |
| 184. C79 | #9294 | semidirect |
| 273. C2×C8 | #11929613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774343 | 2 |
| #23772340 | 2 |
| #23764224 | 2 |
| #23762067 | 2 |
| #23761965 | 2 |
| #23761259 | 2 |
| C79×#1275 | 2 |
| #9294 | 79 |