Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
422 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 111 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. C4⋊C16×D79 | C2 | semidirect |
| 3. #346×D79 | C2 | semidirect |
| 4. #23761359 | C2 | semidirect |
| 5. #23761358 | C2 | semidirect |
| 6. #23761357 | C2 | semidirect |
| 7. C79×#1330 | C2 | semidirect |
| 20. C4⋊(C79⋊C16) | C22 | semidirect |
| 22. #19098339 | C22 | semidirect |
| 25. C4⋊C16×C79 | C22 | semidirect |
| 26. #346×C79 | C22 | semidirect |
| 171. D79 | #1330 | direct (N × H) |
| 178. #1330 | D79 | direct (N × H) |
| 179. C79 | C2×#1330 | semidirect |
| 195. C4⋊C16 | C2×D79 | semidirect |
| 198. #346 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #436×D79 | 2 |
| C4⋊C16×D79 | 2 |
| #346×D79 | 2 |
| #23761359 | 2 |
| #23761358 | 2 |
| #23761357 | 2 |
| C79×#1330 | 2 |
| C2×#1330 | 79 |