Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
368 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 73 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. #23765653 | C2 | semidirect |
| 3. #23765451 | C2 | semidirect |
| 5. #23761450 | C2 | semidirect |
| 6. #23761365 | C2 | semidirect |
| 96. D4×C79 | Q32 | semidirect |
| 146. C79 | #12322 | semidirect |
| 242. D4 | Dic632 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic316 | 2 |
| #23765653 | 2 |
| #23765451 | 2 |
| #23762765 | 2 |
| #23761450 | 2 |
| #23761365 | 2 |
| C79×D4⋊C16 | 2 |
| #12322 | 79 |