Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#19104734 | C2 | semidirect |
| 3. #23781959 | C2 | semidirect |
| 4. #23781954 | C2 | semidirect |
| 5. #23781949 | C2 | semidirect |
| 6. #23781944 | C2 | semidirect |
| 7. #23781708 | C2 | semidirect |
| 8. #23781688 | C2 | semidirect |
| 11. #428×C163 | C2 | semidirect |
| 44. #14579699 | Q8 | semidirect |
| 87. Dic326 | C2×Q8 | semidirect |
| 89. D652 | C2×Q8 | semidirect |
| 138. C163 | #3079 | semidirect |
| 147. #428 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104734 | 2 |
| #23782133 | 2 |
| #23781959 | 2 |
| #23781954 | 2 |
| #23781949 | 2 |
| #23781944 | 2 |
| #23781708 | 2 |
| #23781688 | 2 |
| #23781667 | 2 |
| #23781664 | 2 |
| #428×C163 | 2 |
| #3079 | 163 |