Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
588 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 63 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. #23764753 | C2 | semidirect |
| 2. #23762322 | C2 | semidirect |
| 3. #23762322 | C2 | semidirect |
| 4. #23761397 | C2 | semidirect |
| 5. #23761397 | C2 | semidirect |
| 6. #23761348 | C2 | semidirect |
| 126. C22⋊C4×C79 | SD16 | semidirect |
| 240. C79 | #12242 | semidirect |
| 359. C22⋊C4 | #11929612 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764753 | 2 |
| #23762322 | 2 |
| #23761397 | 2 |
| #23761348 | 2 |
| C79×#2675 | 2 |
| #12242 | 79 |