Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
428 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 145 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. #22553630 | C2 | semidirect |
| 3. #22553597 | C2 | semidirect |
| 4. #22553512 | C2 | semidirect |
| 5. #22553451 | C2 | semidirect |
| 6. C4×#14523500 | C2 | semidirect |
| 7. #22553365 | C2 | semidirect |
| 8. C2×C4×Q8×C131 | C2 | semidirect |
| 76. Q8×C131 | #41 | semidirect |
| 83. C2×C4×C131 | SD16 | semidirect |
| 111. C131 | #3103 | semidirect |
| 114. C2×C4×Q8 | D131 | semidirect |
| 181. Q8 | #14523513 | semidirect |
| 194. C2×C4 | #14523500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553862 | 2 |
| #22553630 | 2 |
| #22553597 | 2 |
| #22553512 | 2 |
| #22553451 | 2 |
| C4×#14523500 | 2 |
| #22553365 | 2 |
| C2×C4×Q8×C131 | 2 |
| #3103 | 131 |