Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
552 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 97 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. #23773120 | C2 | semidirect |
| 3. C2×#19098376 | C2 | semidirect |
| 4. #23765135 | C2 | semidirect |
| 5. #23765028 | C2 | semidirect |
| 6. #23761516 | C2 | semidirect |
| 7. C79×#3058 | C2 | semidirect |
| 41. C2×Dic316 | D4 | semidirect |
| 43. C2×D632 | D4 | semidirect |
| 50. #14579101 | D4 | semidirect |
| 54. #14579097 | D4 | semidirect |
| 214. #3058 | D79 | semidirect |
| 219. C79 | #13310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098999 | 2 |
| #23773120 | 2 |
| C2×#19098376 | 2 |
| #23765135 | 2 |
| #23765028 | 2 |
| #23761516 | 2 |
| C79×#3058 | 2 |
| #13310 | 79 |