Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
316 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23781629 | C2 | semidirect |
| 2. #23781391 | C2 | semidirect |
| 3. #23781389 | C2 | semidirect |
| 50. C23×C163 | M16 | semidirect |
| 67. C2×C4×C163 | M16 | semidirect |
| 97. C163 | #1465 | semidirect |
| 147. C23 | #14579683 | semidirect |
| 164. C2×C4 | #14579683 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23781629 | 2 |
| #23781391 | 2 |
| #23781389 | 2 |
| C2×C4×D4×C163 | 2 |
| #1465 | 163 |