Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
372 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 2. C2×Dic127⋊C8 | C2 | semidirect |
| 5. #22549745 | C2 | semidirect |
| 6. #22549638 | C2 | semidirect |
| 7. #340×C127 | C2 | semidirect |
| 12. #16861171 | C4 | semidirect |
| 67. D508 | C4⋊C4 | semidirect |
| 115. Dic127 | #102 | semidirect |
| 125. C127 | #1802 | semidirect |
| 132. #340 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861171 | 2 |
| C2×Dic127⋊C8 | 2 |
| C2×#16861131 | 2 |
| C2×#16861129 | 2 |
| #22549745 | 2 |
| #22549638 | 2 |
| #340×C127 | 2 |
| #1802 | 127 |