Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 57 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×#19098398 | C2 | semidirect |
| 2. #23765694 | C2 | semidirect |
| 3. #23765520 | C2 | semidirect |
| 4. #23761603 | C2 | semidirect |
| 5. #23761590 | C2 | semidirect |
| 6. #23761589 | C2 | semidirect |
| 7. C79×#2221 | C2 | semidirect |
| 97. #2221 | D79 | semidirect |
| 101. C79 | #13700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098398 | 2 |
| #23765694 | 2 |
| #23765520 | 2 |
| #23761603 | 2 |
| #23761590 | 2 |
| #23761589 | 2 |
| C79×#2221 | 2 |
| #13700 | 79 |