Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
186 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 67 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. #23765282 | C2 | semidirect |
| 3. #23761603 | C2 | semidirect |
| 4. #23761584 | C2 | semidirect |
| 5. #23761583 | C2 | semidirect |
| 6. C4×C79⋊C32 | C2 | semidirect |
| 7. C79×#2178 | C2 | semidirect |
| 10. #19098403 | C4 | semidirect |
| 11. #19098401 | C4 | semidirect |
| 12. #19098400 | C4 | semidirect |
| 13. #19098398 | C4 | semidirect |
| 94. #2178 | D79 | semidirect |
| 99. C79 | #13655 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765707 | 2 |
| #23765282 | 2 |
| #23761603 | 2 |
| #23761584 | 2 |
| #23761583 | 2 |
| C4×C79⋊C32 | 2 |
| C79×#2178 | 2 |
| #13655 | 79 |