Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
390 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 85 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×M16×D127 | C2 | semidirect |
| 3. C2×#16861125 | C2 | semidirect |
| 4. C2×#16861125 | C2 | semidirect |
| 5. #22549839 | C2 | semidirect |
| 6. #22549645 | C2 | semidirect |
| 7. #343×C127 | C2 | semidirect |
| 52. #14523232 | D4 | semidirect |
| 64. M16×C127 | D4 | semidirect |
| 128. C2×D127 | #100 | semidirect |
| 145. C127 | #1900 | semidirect |
| 152. #343 | D127 | semidirect |
| 204. M16 | D508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D127 | 2 |
| C2×#16861184 | 2 |
| C2×#16861125 | 2 |
| #22549839 | 2 |
| #22549645 | 2 |
| #343×C127 | 2 |
| #1900 | 127 |