Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
636 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 1. #23773845 | C2 | semidirect |
| 2. #23773400 | C2 | semidirect |
| 3. #23764199 | C2 | semidirect |
| 4. #23761800 | C2 | semidirect |
| 5. #23761799 | C2 | semidirect |
| 6. #23761230 | C2 | semidirect |
| 7. C79×#3100 | C2 | semidirect |
| 103. C2×C79⋊C8 | D8 | semidirect |
| 224. #3100 | D79 | semidirect |
| 229. C79 | #10032 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773845 | 2 |
| #23773400 | 2 |
| #23764199 | 2 |
| #23761800 | 2 |
| #23761799 | 2 |
| #23761230 | 2 |
| C79×#3100 | 2 |
| #10032 | 79 |