Finite Group DatabasebetaFinite Group DatabasebetaOrder 20288.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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. #23778828 | C2 | semidirect |
| 2. #23778827 | C2 | semidirect |
| 3. #23778813 | C2 | semidirect |
| 4. #23778812 | C2 | semidirect |
| 5. #23778809 | C2 | semidirect |
| 6. #23778801 | C2 | semidirect |
| 7. #23778800 | C2 | semidirect |
| 8. C2×#19099564 | C2 | semidirect |
| 9. Q16×D317 | C2 | semidirect |
| 10. #23778788 | C2 | semidirect |
| 11. #137×C317 | C2 | semidirect |
| 87. C317 | #578 | semidirect |
| 94. #137 | D317 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23778828 | 2 |
| #23778827 | 2 |
| #23778813 | 2 |
| #23778812 | 2 |
| #23778809 | 2 |
| #23778801 | 2 |
| #23778800 | 2 |
| C2×#19099564 | 2 |
| Q16×D317 | 2 |
| #23778788 | 2 |
| #137×C317 | 2 |
| #578 | 317 |