Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
164 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 71 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×#19104674 | C2 | semidirect |
| 2. C22×C163⋊C16 | C2 | semidirect |
| 4. Dic163⋊C16 | C2 | semidirect |
| 5. (C2×D163)⋊C16 | C2 | semidirect |
| 6. #23781440 | C2 | semidirect |
| 7. C22⋊C16×C163 | C2 | semidirect |
| 32. C163⋊C16 | D4 | semidirect |
| 59. C22×C163 | M32 | semidirect |
| 75. C163 | #2168 | semidirect |
| 82. C22⋊C16 | D163 | semidirect |
| 138. C22 | #19104674 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104674 | 2 |
| C22×C163⋊C16 | 2 |
| C8×C22⋊D163 | 2 |
| Dic163⋊C16 | 2 |
| (C2×D163)⋊C16 | 2 |
| #23781440 | 2 |
| C22⋊C16×C163 | 2 |
| #2168 | 163 |