Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
792 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 181 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. C23×Dic262 | C2 | semidirect |
| 2. C22×#14523502 | C2 | semidirect |
| 4. #22553453 | C2 | direct (N × H) |
| 5. C2×#16862171 | C2 | semidirect |
| 6. C2×C22⋊C8×C131 | C2 | semidirect |
| 11. C22×Dic262 | C22 | semidirect |
| 16. C2×#14523502 | C22 | semidirect |
| 21. #16862171 | C22 | semidirect |
| 24. C22⋊C8×C131 | C22 | semidirect |
| 32. C2×Dic262 | D4 | semidirect |
| 62. Dic262 | C2×D4 | semidirect |
| 73. C23×C131 | SD16 | semidirect |
| 89. C22×C131 | C2×SD16 | semidirect |
| 102. C2×C131 | #448 | semidirect |
| 107. C131 | C2×#448 | semidirect |
| 114. C2×C22⋊C8 | D131 | semidirect |
| 132. C22⋊C8 | C2×D131 | semidirect |
| 169. C23 | #14523502 | semidirect |
| 201. C22 | C2×#14523502 | semidirect |
| 211. C2 | #22553453 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic262 | 2 |
| C22×#14523502 | 2 |
| C2×#16862220 | 2 |
| #22553453 | 2 |
| C2×#16862171 | 2 |
| C2×C22⋊C8×C131 | 2 |
| C2×#448 | 131 |