Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
530 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23766210 | C2 | semidirect |
| 3. #23764320 | C2 | semidirect |
| 4. #23761999 | C2 | semidirect |
| 5. #23761264 | C2 | semidirect |
| 6. #23761257 | C2 | semidirect |
| 7. C79×#1514 | C2 | semidirect |
| 9. #19098950 | C4 | semidirect |
| 10. #19098925 | C4 | semidirect |
| 58. #14579072 | C2×C4 | semidirect |
| 64. C4⋊Q8×C79 | C2×C4 | semidirect |
| 65. #127×C79 | C2×C4 | semidirect |
| 226. #1514 | D79 | semidirect |
| 229. C79 | #9381 | semidirect |
| 260. C4⋊Q8 | C4×D79 | semidirect |
| 261. #127 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774383 | 2 |
| #23766210 | 2 |
| #23764320 | 2 |
| #23761999 | 2 |
| #23761264 | 2 |
| #23761257 | 2 |
| C79×#1514 | 2 |
| #9381 | 79 |