Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
1640 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1640 conjugacy classes of subgroups — too many to draw. Only its 565 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. C22×#14523513 | C2 | semidirect |
| 2. #22553893 | C2 | direct (N × H) |
| 3. C2×#16862226 | C2 | semidirect |
| 4. C2×#16862221 | C2 | semidirect |
| 5. C2×#16862220 | C2 | semidirect |
| 6. C22×C4⋊C4×C131 | C2 | semidirect |
| 8. C2×#14523513 | C22 | semidirect |
| 14. #16862226 | C22 | semidirect |
| 15. #16862221 | C22 | semidirect |
| 16. #16862220 | C22 | semidirect |
| 22. C2×C4⋊C4×C131 | C22 | semidirect |
| 40. C22×C4×C131 | D4 | semidirect |
| 65. C2×C4×C131 | C2×D4 | semidirect |
| 84. C2×C131 | #537 | semidirect |
| 89. C131 | C2×#537 | semidirect |
| 96. C22×C4⋊C4 | D131 | semidirect |
| 111. C2×C4⋊C4 | C2×D131 | semidirect |
| 128. C22×C4 | D524 | semidirect |
| 155. C2×C4 | C2×D524 | semidirect |
| 175. C2 | #22553893 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523513 | 2 |
| #22553893 | 2 |
| C2×#16862226 | 2 |
| C2×#16862221 | 2 |
| C2×#16862220 | 2 |
| C22×C4⋊C4×C131 | 2 |
| C2×#537 | 131 |