Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
424 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 71 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. #23765625 | C2 | semidirect |
| 3. #23762786 | C2 | semidirect |
| 4. #23761447 | C2 | semidirect |
| 5. #23761361 | C2 | semidirect |
| 6. #23761354 | C2 | semidirect |
| 7. C79×#2224 | C2 | semidirect |
| 17. C4×C79⋊C16 | C22 | semidirect |
| 18. #19098316 | C22 | semidirect |
| 20. #500×C79 | C22 | semidirect |
| 23. C4⋊C16×C79 | C22 | semidirect |
| 83. D8×C79 | SD16 | semidirect |
| 154. #2224 | D79 | semidirect |
| 159. C79 | #12368 | semidirect |
| 162. #500 | C2×D79 | semidirect |
| 171. C4⋊C16 | C2×D79 | semidirect |
| 227. D8 | #11929611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×D316 | 2 |
| #23765625 | 2 |
| #23762786 | 2 |
| #23761447 | 2 |
| #23761361 | 2 |
| #23761354 | 2 |
| C79×#2224 | 2 |
| #12368 | 79 |