Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23782470 | C2 | semidirect |
| 2. #23782106 | C2 | semidirect |
| 3. #23782100 | C2 | semidirect |
| 4. #23782095 | C2 | semidirect |
| 5. C2×#19104678 | C2 | semidirect |
| 6. #23782082 | C2 | semidirect |
| 7. #578×C163 | C2 | semidirect |
| 12. #19104681 | C22 | semidirect |
| 13. #19104679 | C22 | semidirect |
| 14. #19104678 | C22 | semidirect |
| 15. #19104678 | C22 | semidirect |
| 16. #19104676 | C22 | semidirect |
| 17. #19104675 | C22 | semidirect |
| 18. C2×C163⋊C16 | C22 | semidirect |
| 21. #135×C163 | C22 | semidirect |
| 22. C2×Q16×C163 | C22 | semidirect |
| 74. C163 | #3416 | semidirect |
| 76. #578 | D163 | semidirect |
| 88. #135 | C2×D163 | semidirect |
| 89. C2×Q16 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782470 | 2 |
| #23782106 | 2 |
| #23782100 | 2 |
| #23782095 | 2 |
| C2×#19104678 | 2 |
| #23782082 | 2 |
| #578×C163 | 2 |
| #3416 | 163 |