Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
780 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#19098950 | C2 | semidirect |
| 2. #23771445 | C2 | semidirect |
| 3. #23764225 | C2 | semidirect |
| 4. C2×#19098303 | C2 | semidirect |
| 5. C2×#19098302 | C2 | semidirect |
| 6. #23761282 | C2 | semidirect |
| 7. C2×#496×C79 | C2 | semidirect |
| 53. #14579072 | D4 | semidirect |
| 70. #127×C79 | D4 | semidirect |
| 79. #97×C79 | D4 | semidirect |
| 234. C2×#496 | D79 | semidirect |
| 240. C79 | #10078 | semidirect |
| 286. #127 | C22⋊D79 | semidirect |
| 309. #97 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098950 | 2 |
| #23771445 | 2 |
| #23764225 | 2 |
| C2×#19098303 | 2 |
| C2×#19098302 | 2 |
| #23761282 | 2 |
| C2×#496×C79 | 2 |
| #10078 | 79 |