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. #23773121 | C2 | semidirect |
| 3. #23773049 | C2 | semidirect |
| 4. C2×#19098375 | C2 | semidirect |
| 5. #23765135 | C2 | semidirect |
| 6. #23765029 | C2 | semidirect |
| 7. C79×#1389 | C2 | semidirect |
| 43. C2×Dic316 | D4 | semidirect |
| 51. C2×D632 | D4 | semidirect |
| 75. M32×C79 | D4 | semidirect |
| 78. #108×C79 | D4 | semidirect |
| 218. #1389 | D79 | semidirect |
| 219. C79 | #13310 | semidirect |
| 283. M32 | D316 | semidirect |
| 287. #108 | D316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099001 | 2 |
| #23773121 | 2 |
| #23773049 | 2 |
| C2×#19098375 | 2 |
| #23765135 | 2 |
| #23765029 | 2 |
| C79×#1389 | 2 |
| #13310 | 79 |