Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
212 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 67 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. #23765682 | C2 | semidirect |
| 5. #23761459 | C2 | semidirect |
| 6. #23761456 | C2 | semidirect |
| 7. C79×#1371 | C2 | semidirect |
| 65. C16×C79 | SD16 | semidirect |
| 107. #1371 | D79 | semidirect |
| 110. C79 | #12456 | semidirect |
| 168. C16 | #11929613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765682 | 2 |
| #23765233 | 2 |
| #23762800 | 2 |
| #23762790 | 2 |
| #23761459 | 2 |
| #23761456 | 2 |
| C79×#1371 | 2 |
| #12456 | 79 |