Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
538 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 107 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×#19098674 | C2 | semidirect |
| 3. C2×#19098377 | C2 | semidirect |
| 4. #23764294 | C2 | semidirect |
| 5. #23761498 | C2 | semidirect |
| 6. #23761479 | C2 | semidirect |
| 7. C2×#360×C79 | C2 | semidirect |
| 12. C2×#14579104 | C4 | semidirect |
| 13. C2×#14579102 | C4 | semidirect |
| 45. C2×C79⋊C16 | C2×C4 | semidirect |
| 58. C2×Q16×C79 | C2×C4 | semidirect |
| 60. C2×D8×C79 | C2×C4 | semidirect |
| 182. C2×#360 | D79 | semidirect |
| 186. C79 | #13037 | semidirect |
| 213. C2×Q16 | C4×D79 | semidirect |
| 221. 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 |
| C2×#19098674 | 2 |
| C2×#19098377 | 2 |
| #23764294 | 2 |
| #23761498 | 2 |
| #23761479 | 2 |
| C2×#360×C79 | 2 |
| #13037 | 79 |