Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
1152 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 1152 conjugacy classes of subgroups — too many to draw. Only its 469 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. #22550624 | C2 | direct (N × H) |
| 2. C2×#16861197 | C2 | semidirect |
| 3. C2×#16861194 | C2 | semidirect |
| 4. C2×#16861187 | C2 | semidirect |
| 5. C2×#16861184 | C2 | semidirect |
| 6. C2×#125×C127 | C2 | semidirect |
| 11. #16861197 | C22 | semidirect |
| 12. #16861194 | C22 | semidirect |
| 13. #16861187 | C22 | semidirect |
| 14. #16861184 | C22 | semidirect |
| 19. #125×C127 | C22 | semidirect |
| 71. C2×C127 | #562 | semidirect |
| 76. C127 | C2×#562 | semidirect |
| 78. C2×#125 | D127 | semidirect |
| 87. #125 | C2×D127 | semidirect |
| 148. C2 | #22550624 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550624 | 2 |
| C2×#16861197 | 2 |
| C2×#16861194 | 2 |
| C2×#16861187 | 2 |
| C2×#16861184 | 2 |
| C2×#125×C127 | 2 |
| C2×#562 | 127 |