Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
686 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 99 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. #23772860 | C2 | semidirect |
| 2. #23768301 | C2 | semidirect |
| 3. #23761960 | C2 | semidirect |
| 4. #23761825 | C2 | semidirect |
| 5. #23761792 | C2 | semidirect |
| 6. #23761259 | C2 | semidirect |
| 7. C79×#3100 | C2 | semidirect |
| 54. C4⋊(C79⋊C8) | D4 | semidirect |
| 66. C4⋊Q8×C79 | D4 | semidirect |
| 67. #127×C79 | D4 | semidirect |
| 85. C4×C8×C79 | D4 | semidirect |
| 92. C2×D316 | D8 | semidirect |
| 257. #3100 | D79 | semidirect |
| 264. C79 | #9996 | semidirect |
| 302. C4⋊Q8 | C22⋊D79 | semidirect |
| 303. #127 | C22⋊D79 | semidirect |
| 339. C4×C8 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772860 | 2 |
| #23768301 | 2 |
| #23761960 | 2 |
| #23761825 | 2 |
| #23761792 | 2 |
| #23761259 | 2 |
| C79×#3100 | 2 |
| #9996 | 79 |