Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
576 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #23766559 | C2 | semidirect |
| 3. #23764237 | C2 | semidirect |
| 4. #23761917 | C2 | semidirect |
| 5. #23761305 | C2 | semidirect |
| 6. #23761252 | C2 | semidirect |
| 7. C79×#1510 | C2 | semidirect |
| 9. #19098881 | C4 | semidirect |
| 12. #19098697 | C4 | semidirect |
| 58. C22⋊(C79⋊C8) | C2×C4 | semidirect |
| 64. C22×D4×C79 | C2×C4 | semidirect |
| 71. C2×C4⋊C4×C79 | C2×C4 | semidirect |
| 252. #1510 | D79 | semidirect |
| 256. C79 | #9343 | semidirect |
| 283. C22×D4 | C4×D79 | semidirect |
| 300. C2×C4⋊C4 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774197 | 2 |
| #23766559 | 2 |
| #23764237 | 2 |
| #23761917 | 2 |
| #23761305 | 2 |
| #23761252 | 2 |
| C79×#1510 | 2 |
| #9343 | 79 |