Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
380 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 69 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. #23782465 | C2 | semidirect |
| 2. C2×#19104761 | C2 | semidirect |
| 3. #23782232 | C2 | semidirect |
| 4. #23781683 | C2 | semidirect |
| 5. #23781638 | C2 | semidirect |
| 6. #23781436 | C2 | semidirect |
| 7. #418×C163 | C2 | semidirect |
| 40. C2×Dic326 | D4 | semidirect |
| 42. C2×D652 | D4 | semidirect |
| 55. #14579683 | D4 | semidirect |
| 71. C2×C8×C163 | D4 | semidirect |
| 142. C163 | #2008 | semidirect |
| 148. #418 | D163 | semidirect |
| 210. C2×C8 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782465 | 2 |
| C2×#19104761 | 2 |
| #23782232 | 2 |
| #23781683 | 2 |
| #23781638 | 2 |
| #23781436 | 2 |
| #418×C163 | 2 |
| #2008 | 163 |