Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
428 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×Dic127⋊C8 | C2 | semidirect |
| 3. C2×#16861131 | C2 | semidirect |
| 4. C2×#16861130 | C2 | semidirect |
| 5. C2×#16861129 | C2 | semidirect |
| 6. C4⋊C4×Dic127 | C2 | semidirect |
| 7. C2×#102×C127 | C2 | semidirect |
| 13. #16861205 | C4 | semidirect |
| 46. C4⋊Dic127 | D4 | semidirect |
| 63. C4⋊C4×C127 | D4 | semidirect |
| 137. Dic127 | #102 | semidirect |
| 148. C127 | #1982 | semidirect |
| 154. C2×#102 | D127 | semidirect |
| 208. C4⋊C4 | C22⋊D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861205 | 2 |
| C2×Dic127⋊C8 | 2 |
| C2×#16861131 | 2 |
| C2×#16861130 | 2 |
| C2×#16861129 | 2 |
| C4⋊C4×Dic127 | 2 |
| C2×#102×C127 | 2 |
| #1982 | 127 |