Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
636 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 636 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 |
|---|---|---|
| 1. #23773396 | C2 | semidirect |
| 2. #23764198 | C2 | semidirect |
| 3. #23761799 | C2 | semidirect |
| 4. #23761231 | C2 | semidirect |
| 5. C79×#3150 | C2 | semidirect |
| 83. C2×C8×C79 | D8 | semidirect |
| 149. #3150 | D79 | semidirect |
| 154. C79 | #10032 | semidirect |
| 230. C2×C8 | #11929609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773396 | 2 |
| #23764198 | 2 |
| #23761799 | 2 |
| #23761231 | 2 |
| C79×#3150 | 2 |
| #10032 | 79 |