Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
668 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#14579688 | C2 | semidirect |
| 2. C22×#14579687 | C2 | semidirect |
| 3. C22×#14579684 | C2 | semidirect |
| 4. C2×#19104731 | C2 | semidirect |
| 5. C2×#19104722 | C2 | semidirect |
| 6. #23782053 | C2 | direct (N × H) |
| 7. C2×#19104645 | C2 | semidirect |
| 8. C22×D8×C163 | C2 | semidirect |
| 13. C2×#14579688 | C22 | semidirect |
| 15. C2×#14579687 | C22 | semidirect |
| 17. C2×#14579684 | C22 | semidirect |
| 20. #19104731 | C22 | semidirect |
| 22. #19104722 | C22 | semidirect |
| 25. #19104645 | C22 | semidirect |
| 29. C2×D8×C163 | C22 | semidirect |
| 47. C2×C163⋊C8 | D4 | semidirect |
| 64. C2×C8×C163 | D4 | semidirect |
| 80. C163⋊C8 | C2×D4 | semidirect |
| 98. C8×C163 | C2×D4 | semidirect |
| 118. C2×C163 | #496 | semidirect |
| 122. C163 | C2×#496 | semidirect |
| 127. C22×D8 | D163 | semidirect |
| 144. C2×D8 | C2×D163 | semidirect |
| 184. C2×C8 | C22⋊D163 | semidirect |
| 221. C8 | C2×C22⋊D163 | semidirect |
| 242. C2 | #23782053 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579688 | 2 |
| C22×#14579687 | 2 |
| C22×#14579684 | 2 |
| C2×#19104731 | 2 |
| C2×#19104722 | 2 |
| #23782053 | 2 |
| C2×#19104645 | 2 |
| C22×D8×C163 | 2 |
| C2×#496 | 163 |