Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
386 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 109 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. #23765196 | C2 | semidirect |
| 3. #23761340 | C2 | semidirect |
| 5. C79×#1322 | C2 | semidirect |
| 58. C2×C4×D79 | C16 | semidirect |
| 147. #1322 | D79 | semidirect |
| 149. C79 | #11459 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098615 | 2 |
| #23765196 | 2 |
| #23761340 | 2 |
| #23761323 | 2 |
| C79×#1322 | 2 |
| #11459 | 79 |