Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
208 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 105 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. #23781387 | C2 | semidirect |
| 5. #23781386 | C2 | semidirect |
| 6. #23781386 | C2 | semidirect |
| 7. #322×C163 | C2 | semidirect |
| 51. C8×C163 | M16 | semidirect |
| 66. C163 | #1451 | semidirect |
| 74. #322 | D163 | semidirect |
| 118. C8 | #14579682 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23781716 | 2 |
| C4×#14579682 | 2 |
| C4×C8×D163 | 2 |
| #23781387 | 2 |
| #23781386 | 2 |
| #322×C163 | 2 |
| #1451 | 163 |