Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22553869 | C2 | semidirect |
| 3. #22553654 | C2 | semidirect |
| 4. #22553608 | C2 | semidirect |
| 5. #22553603 | C2 | semidirect |
| 6. #22553523 | C2 | semidirect |
| 7. #22553518 | C2 | semidirect |
| 9. #22553420 | C2 | semidirect |
| 10. #22553414 | C2 | semidirect |
| 11. #432×C131 | C2 | semidirect |
| 136. C131 | #3116 | semidirect |
| 148. #432 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553869 | 2 |
| C4×#14523513 | 2 |
| #22553654 | 2 |
| #22553608 | 2 |
| #22553603 | 2 |
| #22553523 | 2 |
| #22553518 | 2 |
| #22553476 | 2 |
| #22553420 | 2 |
| #22553414 | 2 |
| #432×C131 | 2 |
| #3116 | 131 |