Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
272 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 272 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 |
|---|---|---|
| 61. C4×C163 | #101 | semidirect |
| 69. C163 | #1801 | semidirect |
| 131. C4 | #19104654 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23781689 | 2 |
| C2×#19104654 | 2 |
| #23781434 | 2 |
| C2×C4×Q8×C163 | 2 |
| #1801 | 163 |