Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
492 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 2. #23771992 | C2 | semidirect |
| 3. C2×#19098373 | C2 | semidirect |
| 4. #23765029 | C2 | semidirect |
| 5. #23761516 | C2 | semidirect |
| 6. #23761499 | C2 | semidirect |
| 7. C79×#2145 | C2 | semidirect |
| 12. #19098835 | C4 | semidirect |
| 13. #19098830 | C4 | semidirect |
| 53. #14579097 | C2×C4 | semidirect |
| 65. C2×Q16×C79 | C2×C4 | semidirect |
| 67. C2×D8×C79 | C2×C4 | semidirect |
| 196. #2145 | D79 | semidirect |
| 201. C79 | #13005 | semidirect |
| 234. C2×Q16 | C4×D79 | semidirect |
| 236. C2×D8 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773116 | 2 |
| #23771992 | 2 |
| C2×#19098373 | 2 |
| #23765029 | 2 |
| #23761516 | 2 |
| #23761499 | 2 |
| C79×#2145 | 2 |
| #13005 | 79 |