Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
504 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 95 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. #23761738 | C2 | semidirect |
| 2. #23761344 | C2 | semidirect |
| 3. #23761332 | C2 | semidirect |
| 55. C2×D4×C79 | M16 | semidirect |
| 77. C42×C79 | M16 | semidirect |
| 151. C79 | #11533 | semidirect |
| 200. C2×D4 | #11929608 | semidirect |
| 224. C42 | #11929608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23761738 | 2 |
| #23761344 | 2 |
| #23761332 | 2 |
| C79×#2328 | 2 |
| #11533 | 79 |