Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
240 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 81 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. #23762286 | C2 | semidirect |
| 3. C8×D632 | C2 | semidirect |
| 4. #23761472 | C2 | semidirect |
| 5. #23761362 | C2 | semidirect |
| 6. #23761362 | C2 | semidirect |
| 7. C79×#1312 | C2 | semidirect |
| 51. D632 | M16 | semidirect |
| 87. C8×C79 | D16 | semidirect |
| 118. #1312 | D79 | semidirect |
| 119. C79 | #12069 | semidirect |
| 201. C8 | D1264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D1264 | 2 |
| #23762286 | 2 |
| C8×D632 | 2 |
| #23761472 | 2 |
| #23761362 | 2 |
| C79×#1312 | 2 |
| #12069 | 79 |