Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
346 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 346 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. #23765625 | C2 | semidirect |
| 2. #23765435 | C2 | semidirect |
| 3. #23762755 | C2 | semidirect |
| 4. #23761455 | C2 | semidirect |
| 5. #23761361 | C2 | semidirect |
| 6. D4⋊(C79⋊C16) | C2 | semidirect |
| 7. C79×#3334 | C2 | semidirect |
| 97. D4×C79 | D16 | semidirect |
| 144. #3334 | D79 | semidirect |
| 151. C79 | #12340 | semidirect |
| 246. D4 | #14579102 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765625 | 2 |
| #23765435 | 2 |
| #23762755 | 2 |
| #23761455 | 2 |
| #23761361 | 2 |
| D4⋊(C79⋊C16) | 2 |
| C79×#3334 | 2 |
| #12340 | 79 |