Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
164 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 55 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×#16861152 | C2 | semidirect |
| 2. C22×C127⋊C16 | C2 | semidirect |
| 4. #22549703 | C2 | semidirect |
| 5. #22549680 | C2 | semidirect |
| 6. #22549676 | C2 | semidirect |
| 7. #467×C127 | C2 | semidirect |
| 28. C127⋊C16 | D4 | semidirect |
| 59. C22×C127 | SD32 | semidirect |
| 76. C127 | #2217 | semidirect |
| 79. #467 | D127 | semidirect |
| 138. C22 | #16861152 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861152 | 2 |
| C22×C127⋊C16 | 2 |
| #22550112 | 2 |
| #22549703 | 2 |
| #22549680 | 2 |
| #22549676 | 2 |
| #467×C127 | 2 |
| #2217 | 127 |