Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
392 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 93 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. C22×Dic508 | C2 | semidirect |
| 3. C2×#16861132 | C2 | semidirect |
| 5. #340×C127 | C2 | semidirect |
| 47. C22×D127 | Q16 | semidirect |
| 93. C127 | #2001 | semidirect |
| 98. #340 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic508 | 2 |
| C2×#16861189 | 2 |
| C2×#16861132 | 2 |
| C2×(C2×D127)⋊C8 | 2 |
| #340×C127 | 2 |
| #2001 | 127 |