Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
532 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 99 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×#19099006 | C2 | semidirect |
| 2. C2×#19098839 | C2 | semidirect |
| 4. C2×#19098369 | C2 | semidirect |
| 5. C2×#19098366 | C2 | semidirect |
| 6. C2×#19098348 | C2 | semidirect |
| 7. C79×#1387 | C2 | semidirect |
| 47. C2×Dic316 | D4 | semidirect |
| 75. M32×C79 | D4 | semidirect |
| 78. #108×C79 | D4 | semidirect |
| 218. #1387 | D79 | semidirect |
| 219. C79 | #13308 | semidirect |
| 281. M32 | D316 | semidirect |
| 287. #108 | D316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099006 | 2 |
| C2×#19098839 | 2 |
| #23773072 | 2 |
| C2×#19098369 | 2 |
| C2×#19098366 | 2 |
| C2×#19098348 | 2 |
| C79×#1387 | 2 |
| #13308 | 79 |