Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
820 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 253 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×#16861174 | C2 | semidirect |
| 3. #22549781 | C2 | semidirect |
| 4. #22549780 | C2 | semidirect |
| 10. C22×Dic254 | C4 | semidirect |
| 43. C22⋊Dic127 | Q8 | semidirect |
| 56. Dic254 | C22⋊C4 | semidirect |
| 67. C2×Dic127 | C2×Q8 | semidirect |
| 86. C22×C127 | C4×Q8 | semidirect |
| 106. C127 | Q8×C22⋊C4 | semidirect |
| 192. C22 | #16861174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic254 | 2 |
| C2×#16861174 | 2 |
| #22549781 | 2 |
| #22549780 | 2 |
| #22549734 | 2 |
| C22⋊C4×Dic127 | 2 |
| C4×C22⋊Dic127 | 2 |
| #380×C127 | 2 |
| Q8×C22⋊C4 | 127 |