Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
406 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23765173 | C2 | semidirect |
| 4. #23764149 | C2 | semidirect |
| 5. #23761501 | C2 | semidirect |
| 6. #23761481 | C2 | semidirect |
| 25. #360×C79 | C4 | semidirect |
| 58. M32×C79 | C2×C4 | semidirect |
| 61. #106×C79 | C2×C4 | semidirect |
| 162. C79 | #12951 | semidirect |
| 179. #360 | Dic79 | semidirect |
| 203. M32 | C2×Dic79 | semidirect |
| 211. #106 | C2×Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #135×Dic79 | 2 |
| #23765173 | 2 |
| #23765149 | 2 |
| #23764149 | 2 |
| #23761501 | 2 |
| #23761481 | 2 |
| C79×#2145 | 2 |
| #12951 | 79 |