Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
604 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 105 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. #23774345 | C2 | semidirect |
| 3. #23762082 | C2 | semidirect |
| 4. #23761899 | C2 | semidirect |
| 6. #23761301 | C2 | semidirect |
| 101. C2×D4×C79 | Q16 | semidirect |
| 205. C79 | #10248 | semidirect |
| 285. C2×D4 | #11929614 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774345 | 2 |
| #23768353 | 2 |
| #23762082 | 2 |
| #23761899 | 2 |
| #23761791 | 2 |
| #23761301 | 2 |
| C79×#3077 | 2 |
| #10248 | 79 |