Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
502 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 4. #23762002 | C2 | semidirect |
| 5. #23761266 | C2 | semidirect |
| 6. #23761265 | C2 | semidirect |
| 7. C79×#1528 | C2 | semidirect |
| 220. #1528 | D79 | semidirect |
| 223. C79 | #9189 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772428 | 2 |
| #23769269 | 2 |
| C4×#14579077 | 2 |
| #23762002 | 2 |
| #23761266 | 2 |
| #23761265 | 2 |
| C79×#1528 | 2 |
| #9189 | 79 |