Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 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. C2×#16861230 | C2 | semidirect |
| 2. #22550546 | C2 | semidirect |
| 3. #22550529 | C2 | semidirect |
| 4. #22550102 | C2 | semidirect |
| 5. #22550083 | C2 | semidirect |
| 6. #22550068 | C2 | semidirect |
| 7. #22550035 | C2 | semidirect |
| 8. #22550020 | C2 | semidirect |
| 9. C4×#14523237 | C2 | semidirect |
| 10. C8×D508 | C2 | semidirect |
| 11. #492×C127 | C2 | semidirect |
| 57. #14523237 | D4 | semidirect |
| 127. C4×C127 | #135 | semidirect |
| 141. C127 | #3284 | semidirect |
| 145. #492 | D127 | semidirect |
| 272. 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 |
| #22550546 | 2 |
| #22550529 | 2 |
| #22550102 | 2 |
| #22550083 | 2 |
| #22550068 | 2 |
| #22550035 | 2 |
| #22550020 | 2 |
| C4×#14523237 | 2 |
| C8×D508 | 2 |
| #492×C127 | 2 |
| #3284 | 127 |