Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
136 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 55 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. #23761534 | C2 | semidirect |
| 2. #23761474 | C2 | semidirect |
| 16. D16×C79 | C8 | semidirect |
| 64. C79 | #7385 | semidirect |
| 75. D16 | C79⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23761534 | 2 |
| #23761474 | 2 |
| C4×D16×C79 | 2 |
| #7385 | 79 |