Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
348 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 348 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. #23765072 | C2 | semidirect |
| 2. #23765069 | C2 | semidirect |
| 3. #23761571 | C2 | semidirect |
| 4. #23761563 | C2 | semidirect |
| 12. #540×C79 | C4 | semidirect |
| 14. #496×C79 | C4 | semidirect |
| 17. #488×C79 | C4 | semidirect |
| 22. #433×C79 | C4 | semidirect |
| 35. #127×C79 | C2×C4 | semidirect |
| 38. #125×C79 | C2×C4 | semidirect |
| 54. #97×C79 | C2×C4 | semidirect |
| 55. C4×C8×C79 | C2×C4 | semidirect |
| 165. C79 | #13609 | semidirect |
| 166. #540 | Dic79 | semidirect |
| 168. #496 | Dic79 | semidirect |
| 171. #488 | Dic79 | semidirect |
| 176. #433 | Dic79 | semidirect |
| 189. #127 | C2×Dic79 | semidirect |
| 192. #125 | C2×Dic79 | semidirect |
| 214. #97 | C2×Dic79 | semidirect |
| 215. 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 |
| #23761563 | 2 |
| C79×#3220 | 2 |
| #13609 | 79 |