Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1152 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 1152 conjugacy classes of subgroups — too many to draw. Only its 155 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. C2×#19099305 | C2 | semidirect |
| 2. #23774383 | C2 | semidirect |
| 3. #23762704 | C2 | semidirect |
| 4. #23762688 | C2 | semidirect |
| 5. #23762024 | C2 | semidirect |
| 6. #23761997 | C2 | semidirect |
| 7. C79×#3153 | C2 | semidirect |
| 16. #19098950 | C22 | semidirect |
| 17. #19098925 | C22 | semidirect |
| 21. #19098620 | C22 | semidirect |
| 22. #19098303 | C22 | semidirect |
| 23. #19098302 | C22 | semidirect |
| 26. #532×C79 | C22 | semidirect |
| 28. #497×C79 | C22 | semidirect |
| 29. #496×C79 | C22 | semidirect |
| 31. C4×M16×C79 | C22 | semidirect |
| 60. #14579072 | C23 | semidirect |
| 71. C4⋊Q8×C79 | C23 | semidirect |
| 72. #127×C79 | C23 | semidirect |
| 81. #97×C79 | C23 | semidirect |
| 209. #3153 | D79 | semidirect |
| 214. C79 | #18992 | semidirect |
| 220. #532 | C2×D79 | semidirect |
| 227. #497 | C2×D79 | semidirect |
| 229. #496 | C2×D79 | semidirect |
| 236. C4×M16 | C2×D79 | semidirect |
| 256. C4⋊Q8 | C22×D79 | semidirect |
| 257. #127 | C22×D79 | semidirect |
| 288. #97 | C22×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099305 | 2 |
| #23774383 | 2 |
| #23762704 | 2 |
| #23762688 | 2 |
| #23762024 | 2 |
| #23761997 | 2 |
| C79×#3153 | 2 |
| #18992 | 79 |