Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
530 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 103 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. #23766215 | C2 | semidirect |
| 2. #23764320 | C2 | semidirect |
| 3. #23761998 | C2 | semidirect |
| 4. #23761947 | C2 | semidirect |
| 5. #23761266 | C2 | semidirect |
| 6. #23761255 | C2 | semidirect |
| 25. #496×C79 | C4 | semidirect |
| 26. #489×C79 | C4 | semidirect |
| 60. C4⋊Q8×C79 | C2×C4 | semidirect |
| 61. #127×C79 | C2×C4 | semidirect |
| 78. #97×C79 | C2×C4 | semidirect |
| 229. C79 | #9381 | semidirect |
| 232. #496 | Dic79 | semidirect |
| 233. #489 | Dic79 | semidirect |
| 260. C4⋊Q8 | C2×Dic79 | semidirect |
| 261. #127 | C2×Dic79 | semidirect |
| 292. #97 | C2×Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766215 | 2 |
| #23764320 | 2 |
| #23761998 | 2 |
| #23761947 | 2 |
| #23761266 | 2 |
| #23761255 | 2 |
| C79×#3213 | 2 |
| #9381 | 79 |