Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
232 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 232 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. C2×#19098403 | C2 | semidirect |
| 5. #23765651 | C2 | semidirect |
| 6. #23761533 | C2 | semidirect |
| 7. C2×Q64×C79 | C2 | semidirect |
| 99. C2×Q64 | D79 | semidirect |
| 105. C79 | #13730 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098403 | 2 |
| C2×#19098402 | 2 |
| C2×#19098400 | 2 |
| #23765662 | 2 |
| #23765651 | 2 |
| #23761533 | 2 |
| C2×Q64×C79 | 2 |
| #13730 | 79 |