Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
298 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 69 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. #23776289 | C2 | semidirect |
| 4. #23761454 | C2 | semidirect |
| 5. #23761378 | C2 | semidirect |
| 6. #23761364 | C2 | semidirect |
| 73. Q16×C79 | SD16 | semidirect |
| 135. C79 | #12353 | semidirect |
| 188. Q16 | #11929612 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776289 | 2 |
| #23765623 | 2 |
| #23762757 | 2 |
| #23761454 | 2 |
| #23761378 | 2 |
| #23761364 | 2 |
| C79×#2207 | 2 |
| #12353 | 79 |