Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
412 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 55 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. #23771079 | C2 | semidirect |
| 2. #23764626 | C2 | semidirect |
| 4. #23761427 | C2 | semidirect |
| 5. #23761404 | C2 | semidirect |
| 6. #23761343 | C2 | semidirect |
| 7. C79×#1616 | C2 | semidirect |
| 194. #1616 | D79 | semidirect |
| 199. C79 | #12141 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771079 | 2 |
| #23764626 | 2 |
| #23762335 | 2 |
| #23761427 | 2 |
| #23761404 | 2 |
| #23761343 | 2 |
| C79×#1616 | 2 |
| #12141 | 79 |