Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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×#16861238 | C2 | semidirect |
| 2. Q8×D508 | C2 | semidirect |
| 4. #22550256 | C2 | semidirect |
| 5. #22550135 | C2 | semidirect |
| 6. #22550086 | C2 | semidirect |
| 7. #22550081 | C2 | semidirect |
| 8. #22550039 | C2 | semidirect |
| 9. #22550033 | C2 | semidirect |
| 10. #22549955 | C2 | semidirect |
| 11. C4×SD16×C127 | C2 | semidirect |
| 73. SD16×C127 | D4 | semidirect |
| 123. C4×C127 | #137 | semidirect |
| 135. C127 | #3276 | semidirect |
| 145. C4×SD16 | D127 | semidirect |
| 196. SD16 | D508 | semidirect |
| 261. C4 | #16861238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861238 | 2 |
| Q8×D508 | 2 |
| #22550530 | 2 |
| #22550256 | 2 |
| #22550135 | 2 |
| #22550086 | 2 |
| #22550081 | 2 |
| #22550039 | 2 |
| #22550033 | 2 |
| #22549955 | 2 |
| C4×SD16×C127 | 2 |
| #3276 | 127 |