Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
602 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 602 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. #23773427 | C2 | semidirect |
| 2. #23768754 | C2 | semidirect |
| 3. #23761960 | C2 | semidirect |
| 4. #23761828 | C2 | semidirect |
| 5. #23761791 | C2 | semidirect |
| 6. #23761260 | C2 | semidirect |
| 119. C2×D4×C79 | SD16 | semidirect |
| 240. C79 | #9998 | semidirect |
| 335. C2×D4 | #11929612 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773427 | 2 |
| #23768754 | 2 |
| #23761960 | 2 |
| #23761828 | 2 |
| #23761791 | 2 |
| #23761260 | 2 |
| C79×#3036 | 2 |
| #9998 | 79 |