Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
498 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 105 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. #23772253 | C2 | semidirect |
| 3. #23765136 | C2 | semidirect |
| 4. #23765115 | C2 | semidirect |
| 5. #23761501 | C2 | semidirect |
| 6. #23761486 | C2 | semidirect |
| 7. C79×#1976 | C2 | semidirect |
| 12. C2×#14579104 | C4 | semidirect |
| 13. C2×#14579102 | C4 | semidirect |
| 45. C2×C79⋊C16 | C2×C4 | semidirect |
| 54. C2×Q16×C79 | C2×C4 | semidirect |
| 56. C2×D8×C79 | C2×C4 | semidirect |
| 178. #1976 | D79 | semidirect |
| 181. C79 | #13033 | semidirect |
| 207. C2×Q16 | C4×D79 | semidirect |
| 215. C2×D8 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098998 | 2 |
| #23772253 | 2 |
| #23765136 | 2 |
| #23765115 | 2 |
| #23761501 | 2 |
| #23761486 | 2 |
| C79×#1976 | 2 |
| #13033 | 79 |