Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
724 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 115 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. C4×#14579123 | C2 | semidirect |
| 3. #23764227 | C2 | semidirect |
| 4. #23761894 | C2 | semidirect |
| 5. #23761824 | C2 | semidirect |
| 6. #23761232 | C2 | semidirect |
| 7. C79×#1303 | C2 | semidirect |
| 13. #19098844 | C4 | semidirect |
| 14. #19098759 | C4 | semidirect |
| 34. #14579161 | C2×C4 | semidirect |
| 35. #14579158 | C2×C4 | semidirect |
| 71. C4⋊C8×C79 | C2×C4 | semidirect |
| 118. C4×Dic79 | D8 | semidirect |
| 174. D316 | #104 | semidirect |
| 226. #1303 | D79 | semidirect |
| 228. C79 | #9233 | semidirect |
| 285. C4⋊C8 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773401 | 2 |
| C4×#14579123 | 2 |
| #23764227 | 2 |
| #23761894 | 2 |
| #23761824 | 2 |
| #23761232 | 2 |
| C79×#1303 | 2 |
| #9233 | 79 |