Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
552 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 221 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×#14523496 | C2 | semidirect |
| 3. #22553391 | C2 | direct (N × H) |
| 4. C2×C4⋊(C131⋊C8) | C2 | semidirect |
| 5. C2×(C2×D131)⋊C8 | C2 | semidirect |
| 6. C2×C4×C8×C131 | C2 | semidirect |
| 10. C2×#14523496 | C22 | semidirect |
| 16. C4⋊(C131⋊C8) | C22 | semidirect |
| 17. (C2×D131)⋊C8 | C22 | semidirect |
| 21. C4×C8×C131 | C22 | semidirect |
| 39. C2×C8×C131 | D4 | semidirect |
| 57. C2×C4×C131 | M16 | semidirect |
| 65. C8×C131 | C2×D4 | semidirect |
| 76. C4×C131 | C2×M16 | semidirect |
| 80. C2×C131 | #436 | semidirect |
| 85. C131 | C2×#436 | semidirect |
| 92. C2×C4×C8 | D131 | semidirect |
| 107. C4×C8 | C2×D131 | semidirect |
| 123. C2×C8 | D524 | semidirect |
| 142. C2×C4 | #14523496 | semidirect |
| 151. C8 | C2×D524 | semidirect |
| 163. C4 | C2×#14523496 | semidirect |
| 167. C2 | #22553391 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523496 | 2 |
| C2×C4×D524 | 2 |
| #22553391 | 2 |
| C2×C4⋊(C131⋊C8) | 2 |
| C2×(C2×D131)⋊C8 | 2 |
| C2×C4×C8×C131 | 2 |
| C2×#436 | 131 |