Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
316 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 2. #22553368 | C2 | semidirect |
| 3. C4×#14523496 | C2 | semidirect |
| 4. #22553041 | C2 | semidirect |
| 5. D4⋊(C131⋊C8) | C2 | semidirect |
| 6. #22553039 | C2 | semidirect |
| 7. D4⋊C8×C131 | C2 | semidirect |
| 19. C4⋊(C131⋊C8) | C22 | semidirect |
| 23. C4×C131⋊C8 | C22 | semidirect |
| 25. C4⋊C8×C131 | C22 | semidirect |
| 26. C4×C8×C131 | C22 | semidirect |
| 65. D524 | M16 | semidirect |
| 85. D4×C131 | M16 | semidirect |
| 121. C131 | #1490 | semidirect |
| 129. D4⋊C8 | D131 | semidirect |
| 143. C4⋊C8 | C2×D131 | semidirect |
| 148. C4×C8 | C2×D131 | semidirect |
| 191. D4 | #14523496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×D131 | 2 |
| #22553368 | 2 |
| C4×#14523496 | 2 |
| #22553041 | 2 |
| D4⋊(C131⋊C8) | 2 |
| #22553039 | 2 |
| D4⋊C8×C131 | 2 |
| #1490 | 131 |