Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
582 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 582 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. #23772872 | C2 | semidirect |
| 3. #23761852 | C2 | semidirect |
| 4. #23761275 | C2 | semidirect |
| 5. C79×#1984 | C2 | semidirect |
| 75. C2×Q8×C79 | D8 | semidirect |
| 152. #1984 | D79 | semidirect |
| 155. C79 | #10255 | semidirect |
| 210. C2×Q8 | D632 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774710 | 2 |
| #23772872 | 2 |
| #23761852 | 2 |
| #23761275 | 2 |
| C79×#1984 | 2 |
| #10255 | 79 |