Finite Group DatabasebetaFinite Group DatabasebetaOrder 32576.
190 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 54 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. C2×C4⋊#14523266 | C2 | semidirect |
| 4. C2×C4×#14523266 | C2 | semidirect |
| 5. (C2×#14523266)⋊C4 | C2 | semidirect |
| 6. (C2×#14523266)⋊C4 | C2 | semidirect |
| 19. C22⋊Dic509 | C4 | semidirect |
| 20. #22550838 | C4 | semidirect |
| 21. #22550838 | C4 | semidirect |
| 22. C22⋊C4×C509 | C4 | semidirect |
| 86. C509 | #388 | semidirect |
| 108. C22⋊C4 | #14523266 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#14523266 | 2 |
| C2×C22⋊#14523266 | 2 |
| C2×C4×#14523266 | 2 |
| (C2×#14523266)⋊C4 | 2 |
| C22⋊C4×D509 | 2 |
| #388 | 509 |