Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
182 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 182 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. #22549954 | C2 | semidirect |
| 2. D4×C127⋊C8 | C2 | semidirect |
| 3. #22549629 | C2 | semidirect |
| 4. D4⋊(C127⋊C8) | C2 | semidirect |
| 5. D4⋊(C127⋊C8) | C2 | semidirect |
| 6. #22549598 | C2 | semidirect |
| 46. C127⋊C8 | D8 | semidirect |
| 52. D4×C127 | M16 | semidirect |
| 84. C127 | #1581 | semidirect |
| 131. D4 | #14523232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22549954 | 2 |
| D4×C127⋊C8 | 2 |
| #22549629 | 2 |
| D4⋊(C127⋊C8) | 2 |
| #22549598 | 2 |
| C4×D8×C127 | 2 |
| #1581 | 127 |