Finite Group DatabasebetaFinite Group DatabasebetaOrder 20288.
124 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 48 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×#19099583 | C2 | semidirect |
| 2. C22×#14579268 | C2 | semidirect |
| 3. #23778847 | C2 | semidirect |
| 4. C22⋊#14579268 | C2 | semidirect |
| 5. C22⋊#14579268 | C2 | semidirect |
| 6. #23778835 | C2 | semidirect |
| 24. #14579268 | D4 | semidirect |
| 42. C22×C317 | M16 | semidirect |
| 55. C317 | #435 | semidirect |
| 98. C22 | #19099583 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099583 | 2 |
| C22×#14579268 | 2 |
| #23778847 | 2 |
| C22⋊#14579268 | 2 |
| #23778835 | 2 |
| D4×Dic317 | 2 |
| #435 | 317 |