Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
552 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 552 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. C2×#19099001 | C2 | semidirect |
| 2. #23773120 | C2 | semidirect |
| 3. #23773048 | C2 | semidirect |
| 4. C2×#19098377 | C2 | semidirect |
| 5. #23765137 | C2 | semidirect |
| 6. #23761515 | C2 | semidirect |
| 7. C79×#2117 | C2 | semidirect |
| 42. C2×Dic316 | D4 | semidirect |
| 50. C2×D632 | D4 | semidirect |
| 60. #14579097 | D4 | semidirect |
| 78. M32×C79 | D4 | semidirect |
| 217. #2117 | D79 | semidirect |
| 219. C79 | #13310 | semidirect |
| 283. M32 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099001 | 2 |
| #23773120 | 2 |
| #23773048 | 2 |
| C2×#19098377 | 2 |
| #23765137 | 2 |
| #23761515 | 2 |
| C79×#2117 | 2 |
| #13310 | 79 |