Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#16861230 | C2 | semidirect |
| 2. #22550427 | C2 | semidirect |
| 3. C4×#14523247 | C2 | semidirect |
| 4. #22550101 | C2 | semidirect |
| 5. #22550093 | C2 | semidirect |
| 6. #22550083 | C2 | semidirect |
| 7. #22550077 | C2 | semidirect |
| 8. #22550071 | C2 | semidirect |
| 9. C4⋊C8×D127 | C2 | semidirect |
| 10. #22549871 | C2 | semidirect |
| 11. #461×C127 | C2 | semidirect |
| 47. #14523247 | D4 | semidirect |
| 136. C4×C127 | #135 | semidirect |
| 151. C127 | #3035 | semidirect |
| 158. #461 | D127 | semidirect |
| 292. C4 | #16861230 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861230 | 2 |
| #22550427 | 2 |
| C4×#14523247 | 2 |
| #22550101 | 2 |
| #22550093 | 2 |
| #22550083 | 2 |
| #22550077 | 2 |
| #22550071 | 2 |
| C4⋊C8×D127 | 2 |
| #22549871 | 2 |
| #461×C127 | 2 |
| #3035 | 127 |