Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
502 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 99 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. #23765154 | C2 | semidirect |
| 3. #23762147 | C2 | semidirect |
| 4. #23761447 | C2 | semidirect |
| 5. #23761446 | C2 | semidirect |
| 6. #23761445 | C2 | semidirect |
| 7. C79×#1361 | C2 | semidirect |
| 18. C4⋊(C79⋊C16) | C22 | semidirect |
| 20. #19098316 | C22 | semidirect |
| 23. C4⋊C16×C79 | C22 | semidirect |
| 24. #335×C79 | C22 | semidirect |
| 166. #1361 | D79 | semidirect |
| 167. C79 | #11931 | semidirect |
| 181. C4⋊C16 | C2×D79 | semidirect |
| 183. #335 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #493×D79 | 2 |
| #23765154 | 2 |
| #23762147 | 2 |
| #23761447 | 2 |
| #23761446 | 2 |
| #23761445 | 2 |
| C79×#1361 | 2 |
| #11931 | 79 |