Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
568 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 568 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. #23776536 | C2 | semidirect |
| 2. C2×#19099001 | C2 | semidirect |
| 3. #23773886 | C2 | semidirect |
| 4. #23765137 | C2 | semidirect |
| 5. #23765117 | C2 | semidirect |
| 6. #23764298 | C2 | semidirect |
| 7. C79×#1378 | C2 | semidirect |
| 47. C2×Dic316 | D4 | semidirect |
| 59. C2×D632 | D4 | semidirect |
| 81. M32×C79 | D4 | semidirect |
| 83. C2×C16×C79 | D4 | semidirect |
| 224. #1378 | D79 | semidirect |
| 225. C79 | #13334 | semidirect |
| 295. M32 | D316 | semidirect |
| 297. C2×C16 | D316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776536 | 2 |
| C2×#19099001 | 2 |
| #23773886 | 2 |
| #23765137 | 2 |
| #23765117 | 2 |
| #23764298 | 2 |
| C79×#1378 | 2 |
| #13334 | 79 |