Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
186 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 1. #23765281 | C2 | semidirect |
| 2. #23761604 | C2 | semidirect |
| 3. #23761584 | C2 | semidirect |
| 4. C32×Dic79 | C2 | semidirect |
| 12. Q64×C79 | C4 | semidirect |
| 13. SD64×C79 | C4 | semidirect |
| 14. D32×C79 | C4 | semidirect |
| 68. C79 | #13655 | semidirect |
| 71. Q64 | Dic79 | semidirect |
| 72. SD64 | Dic79 | semidirect |
| 73. D32 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765281 | 2 |
| #23761604 | 2 |
| #23761584 | 2 |
| C32×Dic79 | 2 |
| C79×#2262 | 2 |
| #13655 | 79 |