Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
252 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 71 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. C2×#19098400 | C2 | semidirect |
| 2. C2×#19098398 | C2 | semidirect |
| 3. #23765650 | C2 | semidirect |
| 4. #23761534 | C2 | semidirect |
| 5. C79×#2249 | C2 | semidirect |
| 23. C79⋊C32 | D4 | semidirect |
| 83. #2249 | D79 | semidirect |
| 86. C79 | #13729 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098400 | 2 |
| C2×#19098398 | 2 |
| #23765650 | 2 |
| #23761534 | 2 |
| C79×#2249 | 2 |
| #13729 | 79 |