Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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×#19099004 | C2 | semidirect |
| 3. C2×#19098372 | C2 | semidirect |
| 4. #23765120 | C2 | semidirect |
| 5. C2×#19098345 | C2 | semidirect |
| 6. #23761507 | C2 | semidirect |
| 7. C2×#470×C79 | C2 | semidirect |
| 50. #14579101 | D4 | semidirect |
| 64. C2×Q16×C79 | D4 | semidirect |
| 79. #106×C79 | D4 | semidirect |
| 214. C2×#470 | D79 | semidirect |
| 219. C79 | #13317 | semidirect |
| 256. C2×Q16 | C22⋊D79 | semidirect |
| 289. #106 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099004 | 2 |
| #23773009 | 2 |
| C2×#19098372 | 2 |
| #23765120 | 2 |
| C2×#19098345 | 2 |
| #23761507 | 2 |
| C2×#470×C79 | 2 |
| #13317 | 79 |