Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
356 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 75 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. #23765627 | C2 | semidirect |
| 2. #23765537 | C2 | semidirect |
| 3. #23762789 | C2 | semidirect |
| 4. #23761449 | C2 | semidirect |
| 5. #23761361 | C2 | semidirect |
| 6. D4⋊(C79⋊C16) | C2 | semidirect |
| 75. D8×C79 | SD16 | semidirect |
| 147. C79 | #12371 | semidirect |
| 210. D8 | #11929612 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765627 | 2 |
| #23765537 | 2 |
| #23762789 | 2 |
| #23761449 | 2 |
| #23761361 | 2 |
| D4⋊(C79⋊C16) | 2 |
| C79×#3283 | 2 |
| #12371 | 79 |