Finite Group DatabasebetaFinite Group DatabasebetaOrder 20288.
148 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 45 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. C2×#19099564 | C2 | semidirect |
| 4. #23778705 | C2 | semidirect |
| 5. #23778704 | C2 | semidirect |
| 7. C2×Q16×C317 | C2 | semidirect |
| 45. C2×D317 | Q16 | semidirect |
| 57. C317 | #451 | semidirect |
| 61. C2×Q16 | D317 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D317 | 2 |
| C2×#19099564 | 2 |
| #23778756 | 2 |
| #23778705 | 2 |
| #23778704 | 2 |
| #23778692 | 2 |
| C2×Q16×C317 | 2 |
| #451 | 317 |