Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
374 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 374 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 |
|---|---|---|
| 4. #23781540 | C2 | semidirect |
| 5. #23781537 | C2 | semidirect |
| 6. #23781431 | C2 | semidirect |
| 7. #342×C163 | C2 | semidirect |
| 21. #19104649 | C4 | semidirect |
| 52. C22⋊Dic163 | C2×C4 | semidirect |
| 68. C22⋊C4×C163 | C2×C4 | semidirect |
| 73. C22×D163 | C4⋊C4 | semidirect |
| 94. C2×Dic163 | C4⋊C4 | semidirect |
| 157. C163 | #1867 | semidirect |
| 165. #342 | D163 | semidirect |
| 224. C22⋊C4 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782138 | 2 |
| C2×#19104649 | 2 |
| #23781542 | 2 |
| #23781540 | 2 |
| #23781537 | 2 |
| #23781431 | 2 |
| #342×C163 | 2 |
| #1867 | 163 |