Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
774 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23766241 | C2 | semidirect |
| 2. #23764237 | C2 | semidirect |
| 3. #23763344 | C2 | semidirect |
| 4. #23761916 | C2 | semidirect |
| 5. #23761305 | C2 | semidirect |
| 6. #23761285 | C2 | semidirect |
| 22. C2×AGL(1,ℤ/8)×C79 | C4 | semidirect |
| 27. #417×C79 | C4 | semidirect |
| 155. Q8×C79 | #99 | semidirect |
| 245. C79 | #9368 | semidirect |
| 247. C2×AGL(1,ℤ/8) | Dic79 | semidirect |
| 254. #417 | Dic79 | semidirect |
| 393. Q8 | #14579076 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766241 | 2 |
| #23764237 | 2 |
| #23763344 | 2 |
| #23761916 | 2 |
| #23761305 | 2 |
| #23761285 | 2 |
| C79×#3006 | 2 |
| #9368 | 79 |