Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
552 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 93 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×#19098999 | C2 | semidirect |
| 2. #23773121 | C2 | semidirect |
| 3. #23773044 | C2 | semidirect |
| 4. #23765137 | C2 | semidirect |
| 5. #23765027 | C2 | semidirect |
| 6. #23761514 | C2 | semidirect |
| 7. C2×#361×C79 | C2 | semidirect |
| 42. C2×Dic316 | D4 | semidirect |
| 44. C2×D632 | D4 | semidirect |
| 60. #14579101 | D4 | semidirect |
| 80. #108×C79 | D4 | semidirect |
| 215. C2×#361 | D79 | semidirect |
| 219. C79 | #13310 | semidirect |
| 287. #108 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098999 | 2 |
| #23773121 | 2 |
| #23773044 | 2 |
| #23765137 | 2 |
| #23765027 | 2 |
| #23761514 | 2 |
| C2×#361×C79 | 2 |
| #13310 | 79 |