Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
162 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 73 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×#16861148 | C2 | semidirect |
| 3. C4⋊(C127⋊C16) | C2 | semidirect |
| 4. (C2×D127)⋊C16 | C2 | semidirect |
| 5. C4×C16×C127 | C2 | semidirect |
| 27. C16×C127 | D4 | semidirect |
| 45. C4×C127 | M32 | semidirect |
| 54. C127 | #2169 | semidirect |
| 59. C4×C16 | D127 | semidirect |
| 81. C16 | D508 | semidirect |
| 100. C4 | #16861148 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861148 | 2 |
| C8×D508 | 2 |
| C4⋊(C127⋊C16) | 2 |
| (C2×D127)⋊C16 | 2 |
| C4×C16×C127 | 2 |
| #2169 | 127 |