Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
774 conjugacy classes of subgroups; only the 297 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 297 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×#16861216 | C2 | semidirect |
| 2. #22549843 | C2 | semidirect |
| 3. #22549840 | C2 | semidirect |
| 4. C2×C22⋊(C127⋊C8) | C2 | semidirect |
| 7. C2×#14523232 | C22 | semidirect |
| 8. C22×C127⋊C8 | C22 | semidirect |
| 11. C22⋊(C127⋊C8) | C22 | semidirect |
| 12. C22⋊(C127⋊C8) | C22 | semidirect |
| 76. C22×C127 | #131 | semidirect |
| 89. C127 | #2880 | semidirect |
| 165. C22 | #16861216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861216 | 2 |
| #22549843 | 2 |
| #22549840 | 2 |
| C2×C22⋊(C127⋊C8) | 2 |
| C22×#41×C127 | 2 |
| #2880 | 127 |