Finite Group DatabasebetaFinite Group DatabasebetaOrder 20288.
142 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 39 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 |
|---|---|---|
| 2. #23778811 | C2 | semidirect |
| 3. #23778778 | C2 | semidirect |
| 4. #23778707 | C2 | semidirect |
| 5. #23778706 | C2 | semidirect |
| 6. #23778698 | C2 | semidirect |
| 7. #137×C317 | C2 | semidirect |
| 61. C317 | #456 | semidirect |
| 65. #137 | D317 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23778827 | 2 |
| #23778811 | 2 |
| #23778778 | 2 |
| #23778707 | 2 |
| #23778706 | 2 |
| #23778698 | 2 |
| #137×C317 | 2 |
| #456 | 317 |