Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
408 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 59 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. #23771284 | C2 | semidirect |
| 4. #23761429 | C2 | semidirect |
| 5. #23761426 | C2 | semidirect |
| 6. #23761334 | C2 | semidirect |
| 88. C2×Q8×C79 | SD16 | semidirect |
| 188. C79 | #12128 | semidirect |
| 256. C2×Q8 | #11929612 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771284 | 2 |
| #23762437 | 2 |
| #23762369 | 2 |
| #23761429 | 2 |
| #23761426 | 2 |
| #23761334 | 2 |
| C79×#2007 | 2 |
| #12128 | 79 |