Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
812 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#19098702 | C2 | semidirect |
| 3. #23767054 | C2 | semidirect |
| 4. #23764235 | C2 | semidirect |
| 5. #23761967 | C2 | semidirect |
| 6. #23761247 | C2 | semidirect |
| 7. C79×#1787 | C2 | semidirect |
| 247. #1787 | D79 | semidirect |
| 250. C79 | #9948 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774151 | 2 |
| C2×#19098702 | 2 |
| #23767054 | 2 |
| #23764235 | 2 |
| #23761967 | 2 |
| #23761247 | 2 |
| C79×#1787 | 2 |
| #9948 | 79 |