Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
692 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 83 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. #23774389 | C2 | semidirect |
| 2. #23773491 | C2 | semidirect |
| 3. #23768339 | C2 | semidirect |
| 4. #23764319 | C2 | semidirect |
| 5. #23761997 | C2 | semidirect |
| 6. #23761257 | C2 | semidirect |
| 7. C79×#1490 | C2 | semidirect |
| 40. #14579161 | D4 | semidirect |
| 41. #14579158 | D4 | semidirect |
| 68. #14579072 | D4 | semidirect |
| 80. C4⋊C8×C79 | D4 | semidirect |
| 244. #1490 | D79 | semidirect |
| 246. C79 | #10004 | semidirect |
| 311. C4⋊C8 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774389 | 2 |
| #23773491 | 2 |
| #23768339 | 2 |
| #23764319 | 2 |
| #23761997 | 2 |
| #23761257 | 2 |
| C79×#1490 | 2 |
| #10004 | 79 |