Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
370 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 2. #23782145 | C2 | semidirect |
| 3. C2×#19104661 | C2 | semidirect |
| 4. #23781568 | C2 | semidirect |
| 5. #23781433 | C2 | semidirect |
| 6. #23781424 | C2 | semidirect |
| 7. #418×C163 | C2 | semidirect |
| 10. #19104761 | C4 | semidirect |
| 42. #14579683 | C2×C4 | semidirect |
| 58. C2×D4×C163 | C2×C4 | semidirect |
| 69. Dic326 | C22⋊C4 | semidirect |
| 71. D652 | C22⋊C4 | semidirect |
| 132. C163 | #1883 | semidirect |
| 137. #418 | D163 | semidirect |
| 174. C2×D4 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104761 | 2 |
| #23782145 | 2 |
| C2×#19104661 | 2 |
| #23781568 | 2 |
| #23781433 | 2 |
| #23781424 | 2 |
| #418×C163 | 2 |
| #1883 | 163 |