Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
416 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 2. #23765174 | C2 | semidirect |
| 4. #23764188 | C2 | semidirect |
| 5. #23761515 | C2 | semidirect |
| 6. #23761485 | C2 | semidirect |
| 18. #19098376 | C4 | semidirect |
| 32. #14579101 | C2×C4 | semidirect |
| 35. #14579097 | C2×C4 | semidirect |
| 145. C79 | #12953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772252 | 2 |
| #23765174 | 2 |
| C2×#19098376 | 2 |
| #23764188 | 2 |
| #23761515 | 2 |
| #23761485 | 2 |
| C2×#361×C79 | 2 |
| #12953 | 79 |