Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
602 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 602 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. #23768758 | C2 | semidirect |
| 3. #23761960 | C2 | semidirect |
| 4. #23761829 | C2 | semidirect |
| 5. #23761792 | C2 | semidirect |
| 6. #23761259 | C2 | semidirect |
| 7. C79×#3103 | C2 | semidirect |
| 90. C2×D316 | SD16 | semidirect |
| 233. #3103 | D79 | semidirect |
| 240. C79 | #9998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772860 | 2 |
| #23768758 | 2 |
| #23761960 | 2 |
| #23761829 | 2 |
| #23761792 | 2 |
| #23761259 | 2 |
| C79×#3103 | 2 |
| #9998 | 79 |