Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
648 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 181 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. C22×#14523233 | C2 | semidirect |
| 2. C2×#16861206 | C2 | semidirect |
| 3. #22550071 | C2 | direct (N × H) |
| 4. C2×C4⋊(C127⋊C8) | C2 | semidirect |
| 5. C2×#16861129 | C2 | semidirect |
| 6. C2×C4×D4×C127 | C2 | semidirect |
| 11. C2×#14523233 | C22 | semidirect |
| 14. #16861206 | C22 | semidirect |
| 15. C4⋊(C127⋊C8) | C22 | semidirect |
| 16. #16861129 | C22 | semidirect |
| 20. C4×D4×C127 | C22 | semidirect |
| 39. C2×D4×C127 | D4 | semidirect |
| 69. D4×C127 | C2×D4 | semidirect |
| 74. C2×C4×C127 | D8 | semidirect |
| 96. C4×C127 | C2×D8 | semidirect |
| 100. C2×C127 | #459 | semidirect |
| 106. C127 | C2×#459 | semidirect |
| 109. C2×C4×D4 | D127 | semidirect |
| 124. C4×D4 | C2×D127 | semidirect |
| 142. C2×D4 | D508 | semidirect |
| 174. D4 | C2×D508 | semidirect |
| 179. C2×C4 | #14523233 | semidirect |
| 202. C4 | C2×#14523233 | semidirect |
| 207. C2 | #22550071 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523233 | 2 |
| C2×#16861206 | 2 |
| #22550071 | 2 |
| C2×C4⋊(C127⋊C8) | 2 |
| C2×#16861129 | 2 |
| C2×C4×D4×C127 | 2 |
| C2×#459 | 127 |