Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
344 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 344 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. #23765092 | C2 | semidirect |
| 2. #23765069 | C2 | semidirect |
| 3. #23761575 | C2 | semidirect |
| 4. #23761557 | C2 | semidirect |
| 12. #540×C79 | C4 | semidirect |
| 15. #493×C79 | C4 | semidirect |
| 16. #490×C79 | C4 | semidirect |
| 22. #433×C79 | C4 | semidirect |
| 36. #127×C79 | C2×C4 | semidirect |
| 38. #125×C79 | C2×C4 | semidirect |
| 54. #97×C79 | C2×C4 | semidirect |
| 55. C4×C8×C79 | C2×C4 | semidirect |
| 164. C79 | #13605 | semidirect |
| 165. #540 | Dic79 | semidirect |
| 168. #493 | Dic79 | semidirect |
| 169. #490 | Dic79 | semidirect |
| 175. #433 | Dic79 | semidirect |
| 190. #127 | C2×Dic79 | semidirect |
| 192. #125 | C2×Dic79 | semidirect |
| 213. #97 | C2×Dic79 | semidirect |
| 214. C4×C8 | C2×Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765092 | 2 |
| #23765069 | 2 |
| #23761575 | 2 |
| #23761557 | 2 |
| C79×#3220 | 2 |
| #13605 | 79 |