Finite Group DatabasebetaFinite Group DatabasebetaOrder 20288.
322 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 127 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. C22×Dic634 | C2 | semidirect |
| 3. #23778758 | C2 | direct (N × H) |
| 4. C2×#19099553 | C2 | semidirect |
| 5. C2×#19099553 | C2 | semidirect |
| 8. C2×C4⋊C4×C317 | C2 | semidirect |
| 11. C2×Dic634 | C22 | semidirect |
| 17. #19099553 | C22 | semidirect |
| 18. #19099553 | C22 | semidirect |
| 24. C4⋊C4×C317 | C22 | semidirect |
| 27. C22×D317 | Q8 | semidirect |
| 51. C2×D317 | C2×Q8 | semidirect |
| 58. C2×C317 | C22⋊Q8 | semidirect |
| 63. C317 | C2×C22⋊Q8 | semidirect |
| 70. C2×C4⋊C4 | D317 | semidirect |
| 86. C4⋊C4 | C2×D317 | semidirect |
| 123. C2 | #23778758 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic634 | 2 |
| C22×C4×D317 | 2 |
| #23778758 | 2 |
| C2×#19099553 | 2 |
| C2×#19099551 | 2 |
| C2×C4⋊C4×C317 | 2 |
| C2×C22⋊Q8 | 317 |