Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
174 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 57 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×#16861152 | C2 | semidirect |
| 3. C4⋊(C127⋊C16) | C2 | semidirect |
| 4. #22549676 | C2 | semidirect |
| 5. C4×Q16×C127 | C2 | semidirect |
| 25. Q16×C127 | D4 | semidirect |
| 54. C4×C127 | SD32 | semidirect |
| 62. C127 | #2207 | semidirect |
| 65. C4×Q16 | D127 | semidirect |
| 83. Q16 | D508 | semidirect |
| 116. C4 | #16861152 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861152 | 2 |
| #22550253 | 2 |
| C4⋊(C127⋊C16) | 2 |
| #22549676 | 2 |
| C4×Q16×C127 | 2 |
| #2207 | 127 |