Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
752 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 103 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. #23765055 | C2 | semidirect |
| 3. #23765051 | C2 | semidirect |
| 4. #23763950 | C2 | semidirect |
| 5. #23763945 | C2 | semidirect |
| 6. #23763784 | C2 | semidirect |
| 7. C79×#2132 | C2 | semidirect |
| 10. #19099300 | C4 | semidirect |
| 14. #19099243 | C4 | semidirect |
| 285. #2132 | D79 | semidirect |
| 291. C79 | #12770 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777827 | 2 |
| #23765055 | 2 |
| #23765051 | 2 |
| #23763950 | 2 |
| #23763945 | 2 |
| #23763784 | 2 |
| C79×#2132 | 2 |
| #12770 | 79 |