Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
148 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 10. #19104681 | C4 | semidirect |
| 63. C163 | #2176 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104681 | 2 |
| C4×Dic652 | 2 |
| #23781492 | 2 |
| #23781469 | 2 |
| #23781468 | 2 |
| #23781441 | 2 |
| C4×Q16×C163 | 2 |
| #2176 | 163 |