Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
610 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23764240 | C2 | semidirect |
| 3. #23762158 | C2 | semidirect |
| 4. #23762069 | C2 | semidirect |
| 5. #23762068 | C2 | semidirect |
| 6. M16×C79⋊C8 | C2 | semidirect |
| 7. C79×#1965 | C2 | semidirect |
| 97. M16×C79 | D8 | semidirect |
| 142. C79⋊C8 | #100 | semidirect |
| 171. #1965 | D79 | semidirect |
| 176. C79 | #9802 | semidirect |
| 261. M16 | #11929609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098939 | 2 |
| #23764240 | 2 |
| #23762158 | 2 |
| #23762069 | 2 |
| #23762068 | 2 |
| M16×C79⋊C8 | 2 |
| C79×#1965 | 2 |
| #9802 | 79 |