Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
908 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 191 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. #23772304 | C2 | semidirect |
| 2. #23772105 | C2 | semidirect |
| 3. #23764954 | C2 | semidirect |
| 4. #23764917 | C2 | semidirect |
| 5. #23764505 | C2 | semidirect |
| 6. #23764468 | C2 | semidirect |
| 7. C79×#1747 | C2 | semidirect |
| 50. #97×C79 | D4 | semidirect |
| 51. C4×C8×C79 | D4 | semidirect |
| 130. #1747 | D79 | semidirect |
| 131. C79 | #23795 | semidirect |
| 174. #97 | D316 | semidirect |
| 175. C4×C8 | D316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772304 | 2 |
| #23772105 | 2 |
| #23764954 | 2 |
| #23764917 | 2 |
| #23764505 | 2 |
| #23764468 | 2 |
| C79×#1747 | 2 |
| #23795 | 79 |