Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
412 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 2. #22550272 | C2 | semidirect |
| 3. #22550250 | C2 | semidirect |
| 4. #22550226 | C2 | semidirect |
| 5. #22550224 | C2 | semidirect |
| 6. #22550107 | C2 | semidirect |
| 7. C4×#14523235 | C2 | semidirect |
| 8. C2×C4×C127⋊C8 | C2 | semidirect |
| 9. #533×C127 | C2 | semidirect |
| 76. C127⋊C8 | #41 | semidirect |
| 84. C2×C4×C127 | SD16 | semidirect |
| 113. C127 | #3167 | semidirect |
| 114. #533 | D127 | semidirect |
| 195. C2×C4 | #14523235 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550426 | 2 |
| #22550272 | 2 |
| #22550250 | 2 |
| #22550226 | 2 |
| #22550224 | 2 |
| #22550107 | 2 |
| C4×#14523235 | 2 |
| C2×C4×C127⋊C8 | 2 |
| #533×C127 | 2 |
| #3167 | 127 |