Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
460 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 57 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. #23762376 | C2 | semidirect |
| 4. #23762373 | C2 | semidirect |
| 5. #23761429 | C2 | semidirect |
| 7. C79×#1354 | C2 | semidirect |
| 72. C2×D316 | Q16 | semidirect |
| 194. #1354 | D79 | semidirect |
| 196. C79 | #12220 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23769774 | 2 |
| #23764557 | 2 |
| #23762376 | 2 |
| #23762373 | 2 |
| #23761429 | 2 |
| #23761331 | 2 |
| C79×#1354 | 2 |
| #12220 | 79 |