Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
512 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 113 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. #23771996 | C2 | semidirect |
| 3. #23765117 | C2 | semidirect |
| 4. C2×#19098363 | C2 | semidirect |
| 5. C2×#19098348 | C2 | semidirect |
| 6. #23761497 | C2 | semidirect |
| 7. C79×#1387 | C2 | semidirect |
| 14. #19098834 | C4 | semidirect |
| 39. C2×D632 | C2×C4 | semidirect |
| 69. #108×C79 | C2×C4 | semidirect |
| 194. #1387 | D79 | semidirect |
| 196. C79 | #12996 | semidirect |
| 252. #108 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098834 | 2 |
| #23771996 | 2 |
| #23765117 | 2 |
| C2×#19098363 | 2 |
| C2×#19098348 | 2 |
| #23761497 | 2 |
| C79×#1387 | 2 |
| #12996 | 79 |