Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
248 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 4. #23761321 | C2 | semidirect |
| 5. #23761320 | C2 | semidirect |
| 6. #23761320 | C2 | semidirect |
| 7. C79×#1313 | C2 | semidirect |
| 64. C16×C79 | M16 | semidirect |
| 106. #1313 | D79 | semidirect |
| 107. C79 | #11414 | semidirect |
| 164. C16 | #11929607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765201 | 2 |
| #23764993 | 2 |
| #23761686 | 2 |
| #23761321 | 2 |
| #23761320 | 2 |
| C79×#1313 | 2 |
| #11414 | 79 |