Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
498 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23765199 | C2 | semidirect |
| 3. #23761445 | C2 | semidirect |
| 4. C79×#1567 | C2 | semidirect |
| 12. C4⋊(C79⋊C16) | C22 | semidirect |
| 18. #335×C79 | C22 | semidirect |
| 128. #1567 | D79 | semidirect |
| 130. C79 | #11961 | semidirect |
| 144. #335 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098940 | 2 |
| #23765199 | 2 |
| #23761445 | 2 |
| C79×#1567 | 2 |
| #11961 | 79 |