Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
372 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 372 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 |
|---|---|---|
| 2. #23764562 | C2 | semidirect |
| 3. #23762376 | C2 | semidirect |
| 5. #23761429 | C2 | semidirect |
| 6. #23761333 | C2 | semidirect |
| 188. C79 | #12275 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771571 | 2 |
| #23764562 | 2 |
| #23762376 | 2 |
| #23762339 | 2 |
| #23761429 | 2 |
| #23761333 | 2 |
| C79×#1345 | 2 |
| #12275 | 79 |