Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
372 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 107 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. #23761363 | C2 | semidirect |
| 4. #23761360 | C2 | semidirect |
| 5. C79×#1567 | C2 | semidirect |
| 65. Dic316 | M16 | semidirect |
| 68. D632 | M16 | semidirect |
| 153. #1567 | D79 | semidirect |
| 156. C79 | #11660 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14579183 | 2 |
| #23765199 | 2 |
| #23761363 | 2 |
| #23761360 | 2 |
| C79×#1567 | 2 |
| #11660 | 79 |