Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
254 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 87 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. C8×D632 | C2 | semidirect |
| 3. #23761473 | C2 | semidirect |
| 4. #23761361 | C2 | semidirect |
| 5. #23761360 | C2 | semidirect |
| 6. #23761317 | C2 | semidirect |
| 7. C8×D8×C79 | C2 | semidirect |
| 26. #14579102 | C8 | semidirect |
| 47. D632 | C2×C8 | semidirect |
| 54. C79⋊C16 | C2×C8 | semidirect |
| 58. D8×C79 | C2×C8 | semidirect |
| 114. C8×D8 | D79 | semidirect |
| 119. C79 | #12045 | semidirect |
| 163. D8 | C8×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14579102 | 2 |
| C8×D632 | 2 |
| #23761473 | 2 |
| #23761361 | 2 |
| #23761360 | 2 |
| #23761317 | 2 |
| C8×D8×C79 | 2 |
| #12045 | 79 |