Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 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×#16861236 | C2 | semidirect |
| 2. #22550427 | C2 | semidirect |
| 3. C4×D4×D127 | C2 | semidirect |
| 4. #22550094 | C2 | semidirect |
| 5. #22550093 | C2 | semidirect |
| 6. #22550078 | C2 | semidirect |
| 7. #22550072 | C2 | semidirect |
| 8. #22550071 | C2 | semidirect |
| 9. #22549898 | C2 | semidirect |
| 10. #22549876 | C2 | semidirect |
| 11. #461×C127 | C2 | semidirect |
| 20. #16861206 | C22 | semidirect |
| 21. #16861198 | C22 | semidirect |
| 34. C4⋊(C127⋊C8) | C22 | semidirect |
| 35. Dic127⋊C8 | C22 | semidirect |
| 36. #16861133 | C22 | semidirect |
| 37. #16861131 | C22 | semidirect |
| 38. #16861129 | C22 | semidirect |
| 40. C4⋊Q8×C127 | C22 | semidirect |
| 42. C4⋊C8×C127 | C22 | semidirect |
| 43. #103×C127 | C22 | semidirect |
| 54. D4×D127 | D4 | semidirect |
| 146. C4×C127 | AGL(1,ℤ/8) | semidirect |
| 161. C127 | #3036 | semidirect |
| 168. #461 | D127 | semidirect |
| 182. C4⋊Q8 | C2×D127 | semidirect |
| 200. C4⋊C8 | C2×D127 | semidirect |
| 202. #103 | C2×D127 | semidirect |
| 311. C4 | #16861236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861236 | 2 |
| #22550427 | 2 |
| C4×D4×D127 | 2 |
| #22550094 | 2 |
| #22550093 | 2 |
| #22550078 | 2 |
| #22550072 | 2 |
| #22550071 | 2 |
| #22549898 | 2 |
| #22549876 | 2 |
| #461×C127 | 2 |
| #3036 | 127 |