Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
254 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 83 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. D8×C79⋊C8 | C2 | semidirect |
| 3. #23762194 | C2 | semidirect |
| 4. #23761473 | C2 | semidirect |
| 5. #23761362 | C2 | semidirect |
| 6. #23761316 | C2 | semidirect |
| 7. C79×#1331 | C2 | semidirect |
| 27. #14579102 | C8 | semidirect |
| 47. D632 | C2×C8 | semidirect |
| 57. C79⋊C16 | C2×C8 | semidirect |
| 61. D8×C79 | C2×C8 | semidirect |
| 117. #1331 | 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 |
| D8×C79⋊C8 | 2 |
| #23762194 | 2 |
| #23761473 | 2 |
| #23761362 | 2 |
| #23761316 | 2 |
| C79×#1331 | 2 |
| #12045 | 79 |