Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
254 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 99 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. D8×C79⋊C8 | C2 | semidirect |
| 2. #23761474 | C2 | semidirect |
| 3. #23761361 | C2 | semidirect |
| 4. #23761316 | C2 | semidirect |
| 24. D16×C79 | C8 | semidirect |
| 38. D8×C79 | C2×C8 | semidirect |
| 45. C16×C79 | C2×C8 | semidirect |
| 80. C79 | #12045 | semidirect |
| 94. D16 | C79⋊C8 | semidirect |
| 108. D8 | C2×C79⋊C8 | semidirect |
| 120. C16 | C2×C79⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×C79⋊C8 | 2 |
| #23761474 | 2 |
| #23761361 | 2 |
| #23761316 | 2 |
| C4×D16×C79 | 2 |
| #12045 | 79 |