Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
658 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 658 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 |
|---|---|---|
| 1. #23772868 | C2 | semidirect |
| 2. #23768403 | C2 | semidirect |
| 3. #23762068 | C2 | semidirect |
| 4. #23761895 | C2 | semidirect |
| 5. #23761794 | C2 | semidirect |
| 6. #23761302 | C2 | semidirect |
| 84. C2×Dic158 | D8 | semidirect |
| 234. C79 | #10242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772868 | 2 |
| #23768403 | 2 |
| #23762068 | 2 |
| #23761895 | 2 |
| #23761794 | 2 |
| #23761302 | 2 |
| C79×#3205 | 2 |
| #10242 | 79 |