Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
266 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 266 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. #22549900 | C2 | semidirect |
| 2. C4×#14523232 | C2 | semidirect |
| 3. Q8⋊(C127⋊C8) | C2 | semidirect |
| 4. D4⋊(C127⋊C8) | C2 | semidirect |
| 57. Q8×C127 | M16 | semidirect |
| 60. D4×C127 | M16 | semidirect |
| 103. C127 | #1489 | semidirect |
| 158. Q8 | #14523232 | semidirect |
| 161. D4 | #14523232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22549900 | 2 |
| C4×#14523232 | 2 |
| Q8⋊(C127⋊C8) | 2 |
| D4⋊(C127⋊C8) | 2 |
| C4×#41×C127 | 2 |
| #1489 | 127 |