Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
576 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 81 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. #23773787 | C2 | semidirect |
| 2. #23773500 | C2 | semidirect |
| 4. #23762023 | C2 | semidirect |
| 5. #23761950 | C2 | semidirect |
| 6. #23761844 | C2 | semidirect |
| 7. C79×#1288 | C2 | semidirect |
| 39. #14579161 | D4 | semidirect |
| 40. #14579161 | D4 | semidirect |
| 77. #97×C79 | D4 | semidirect |
| 78. C4×C8×C79 | D4 | semidirect |
| 217. #1288 | D79 | semidirect |
| 218. C79 | #10022 | semidirect |
| 287. #97 | D316 | semidirect |
| 288. C4×C8 | D316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773787 | 2 |
| #23773500 | 2 |
| #23769255 | 2 |
| #23762023 | 2 |
| #23761950 | 2 |
| #23761844 | 2 |
| C79×#1288 | 2 |
| #10022 | 79 |