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. #23765137 | C2 | semidirect |
| 4. #23765117 | C2 | semidirect |
| 5. #23764298 | C2 | semidirect |
| 6. #23761502 | C2 | semidirect |
| 7. C79×#1378 | C2 | semidirect |
| 13. C2×#14579106 | C4 | semidirect |
| 14. C2×D1264 | C4 | semidirect |
| 33. C2×Dic316 | C2×C4 | semidirect |
| 39. C2×D632 | C2×C4 | semidirect |
| 64. C2×C16×C79 | C2×C4 | semidirect |
| 180. #1378 | D79 | semidirect |
| 181. C79 | #13033 | semidirect |
| 231. C2×C16 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099001 | 2 |
| #23772253 | 2 |
| #23765137 | 2 |
| #23765117 | 2 |
| #23764298 | 2 |
| #23761502 | 2 |
| C79×#1378 | 2 |
| #13033 | 79 |