Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
760 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23764386 | C2 | semidirect |
| 4. #23761920 | C2 | semidirect |
| 5. #23761305 | C2 | semidirect |
| 6. #23761285 | C2 | semidirect |
| 22. C2×#137×C79 | C4 | semidirect |
| 27. #417×C79 | C4 | semidirect |
| 53. C22×Q8×C79 | C2×C4 | semidirect |
| 62. C2×M16×C79 | C2×C4 | semidirect |
| 68. C2×C4⋊C4×C79 | C2×C4 | semidirect |
| 234. C79 | #9361 | semidirect |
| 236. C2×#137 | Dic79 | semidirect |
| 243. #417 | Dic79 | semidirect |
| 261. C22×Q8 | C2×Dic79 | semidirect |
| 272. C2×M16 | C2×Dic79 | semidirect |
| 280. C2×C4⋊C4 | C2×Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766230 | 2 |
| #23764386 | 2 |
| #23763344 | 2 |
| #23761920 | 2 |
| #23761305 | 2 |
| #23761285 | 2 |
| C79×#3007 | 2 |
| #9361 | 79 |