Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
248 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 75 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. #23762760 | C2 | semidirect |
| 3. #23761472 | C2 | semidirect |
| 4. #23761447 | C2 | semidirect |
| 5. Q8×C16×C79 | C2 | semidirect |
| 51. C16×C79 | SD16 | semidirect |
| 54. Q8×C79 | D16 | semidirect |
| 87. Q8×C16 | D79 | semidirect |
| 91. C79 | #12439 | semidirect |
| 137. C16 | #11929611 | semidirect |
| 140. Q8 | D1264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765650 | 2 |
| #23762760 | 2 |
| #23761472 | 2 |
| #23761447 | 2 |
| Q8×C16×C79 | 2 |
| #12439 | 79 |