Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
222 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 3. #23761469 | C2 | semidirect |
| 4. Q8⋊(C79⋊C16) | C2 | semidirect |
| 6. #23761319 | C2 | semidirect |
| 7. Q8×C16×C79 | C2 | semidirect |
| 70. Q8×C79 | M32 | semidirect |
| 106. Q8×C16 | D79 | semidirect |
| 113. C79 | #12056 | semidirect |
| 176. Q8 | #14579100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765233 | 2 |
| C8×#11929611 | 2 |
| #23761469 | 2 |
| Q8⋊(C79⋊C16) | 2 |
| #23761354 | 2 |
| #23761319 | 2 |
| Q8×C16×C79 | 2 |
| #12056 | 79 |