Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
360 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 67 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. #23765333 | C2 | semidirect |
| 3. #23764723 | C2 | semidirect |
| 4. #23761412 | C2 | semidirect |
| 6. #23761340 | C2 | semidirect |
| 175. C79 | #12163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765333 | 2 |
| #23765316 | 2 |
| #23764723 | 2 |
| #23761412 | 2 |
| #23761409 | 2 |
| #23761340 | 2 |
| C79×#3250 | 2 |
| #12163 | 79 |