Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
604 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 1. C2×#19098999 | C2 | semidirect |
| 2. #23773009 | C2 | semidirect |
| 3. C2×#19098372 | C2 | semidirect |
| 4. #23765116 | C2 | semidirect |
| 5. C2×#19098345 | C2 | semidirect |
| 6. #23761507 | C2 | semidirect |
| 7. C2×#469×C79 | C2 | semidirect |
| 36. C2×Dic316 | D4 | semidirect |
| 38. C2×D632 | D4 | semidirect |
| 50. #14579101 | D4 | semidirect |
| 53. #14579095 | D4 | semidirect |
| 65. C2×D8×C79 | D4 | semidirect |
| 79. #106×C79 | D4 | semidirect |
| 223. C2×#469 | D79 | semidirect |
| 228. C79 | #13316 | semidirect |
| 268. C2×D8 | C22⋊D79 | semidirect |
| 298. #106 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098999 | 2 |
| #23773009 | 2 |
| C2×#19098372 | 2 |
| #23765116 | 2 |
| C2×#19098345 | 2 |
| #23761507 | 2 |
| C2×#469×C79 | 2 |
| #13316 | 79 |