Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
654 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 654 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. #23774405 | C2 | semidirect |
| 2. #23773499 | C2 | semidirect |
| 4. #23764344 | C2 | semidirect |
| 5. #23761997 | C2 | semidirect |
| 6. #23761257 | C2 | semidirect |
| 7. C79×#1490 | C2 | semidirect |
| 39. #14579161 | D4 | semidirect |
| 40. #14579161 | D4 | semidirect |
| 67. #14579072 | D4 | semidirect |
| 79. C4⋊C8×C79 | D4 | semidirect |
| 233. #1490 | D79 | semidirect |
| 235. C79 | #10008 | semidirect |
| 300. C4⋊C8 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774405 | 2 |
| #23773499 | 2 |
| #23768339 | 2 |
| #23764344 | 2 |
| #23761997 | 2 |
| #23761257 | 2 |
| C79×#1490 | 2 |
| #10008 | 79 |