Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
314 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 93 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. #23765197 | C2 | semidirect |
| 3. #23765154 | C2 | semidirect |
| 4. Q8⋊(C79⋊C16) | C2 | semidirect |
| 5. #23761356 | C2 | semidirect |
| 6. #23761354 | C2 | semidirect |
| 7. C79×Q8⋊C16 | C2 | semidirect |
| 158. Q8⋊C16 | D79 | semidirect |
| 161. C79 | #11624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772377 | 2 |
| #23765197 | 2 |
| #23765154 | 2 |
| Q8⋊(C79⋊C16) | 2 |
| #23761356 | 2 |
| #23761354 | 2 |
| C79×Q8⋊C16 | 2 |
| #11624 | 79 |