Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
592 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 133 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×#16861132 | C2 | semidirect |
| 8. C22×Dic254 | C4 | semidirect |
| 43. Dic254 | C22⋊C4 | semidirect |
| 68. C22×C127 | #103 | semidirect |
| 86. C127 | #1787 | semidirect |
| 154. C22 | #16861132 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic254 | 2 |
| C2×#16861132 | 2 |
| C2×C22⋊(C127⋊C8) | 2 |
| #380×C127 | 2 |
| #1787 | 127 |