Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
336 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 336 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 |
|---|---|---|
| 3. #23761571 | C2 | semidirect |
| 4. #23761565 | C2 | semidirect |
| 12. #541×C79 | C4 | semidirect |
| 14. #497×C79 | C4 | semidirect |
| 17. #488×C79 | C4 | semidirect |
| 22. #433×C79 | C4 | semidirect |
| 35. C4⋊Q8×C79 | C2×C4 | semidirect |
| 40. #125×C79 | C2×C4 | semidirect |
| 54. #97×C79 | C2×C4 | semidirect |
| 55. C4×C8×C79 | C2×C4 | semidirect |
| 159. C79 | #13610 | semidirect |
| 160. #541 | Dic79 | semidirect |
| 162. #497 | Dic79 | semidirect |
| 165. #488 | Dic79 | semidirect |
| 170. #433 | Dic79 | semidirect |
| 183. C4⋊Q8 | C2×Dic79 | semidirect |
| 188. #125 | C2×Dic79 | semidirect |
| 208. #97 | C2×Dic79 | semidirect |
| 209. C4×C8 | C2×Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765072 | 2 |
| #23765069 | 2 |
| #23761571 | 2 |
| #23761565 | 2 |
| C79×#3222 | 2 |
| #13610 | 79 |