Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
302 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 93 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. #23781708 | C2 | semidirect |
| 4. #23781534 | C2 | semidirect |
| 5. #23781434 | C2 | semidirect |
| 6. #23781424 | C2 | semidirect |
| 15. #19104662 | C4 | semidirect |
| 31. #14579683 | C2×C4 | semidirect |
| 38. C4×Dic163 | C2×C4 | semidirect |
| 69. Q8×C163 | C4⋊C4 | semidirect |
| 73. D4×C163 | C4⋊C4 | semidirect |
| 112. C163 | #1859 | semidirect |
| 175. Q8 | Dic163⋊C4 | semidirect |
| 179. D4 | Dic163⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23781708 | 2 |
| C2×#19104662 | 2 |
| #23781666 | 2 |
| #23781534 | 2 |
| #23781434 | 2 |
| #23781424 | 2 |
| #520×C163 | 2 |
| #1859 | 163 |