Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
242 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 101 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. Q16×C79⋊C8 | C2 | semidirect |
| 3. #23761474 | C2 | semidirect |
| 4. #23761364 | C2 | semidirect |
| 6. C16×C79⋊C8 | C2 | semidirect |
| 36. SD32×C79 | C8 | semidirect |
| 55. Q16×C79 | C2×C8 | semidirect |
| 67. C16×C79 | C2×C8 | semidirect |
| 88. C79⋊C8 | SD32 | direct (N × H) |
| 113. C79 | C8×SD32 | semidirect |
| 134. SD32 | C79⋊C8 | direct (N × H) |
| 154. Q16 | C2×C79⋊C8 | semidirect |
| 173. C16 | C2×C79⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×C79⋊C8 | 2 |
| D8×C79⋊C8 | 2 |
| #23761474 | 2 |
| #23761364 | 2 |
| #23761361 | 2 |
| C16×C79⋊C8 | 2 |
| C4×SD32×C79 | 2 |
| C8×SD32 | 79 |