Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
474 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 85. M16×C67 | Q16 | semidirect |
| 146. C67 | #9798 | semidirect |
| 215. M16 | #11761618 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863775 | 2 |
| #22561198 | 2 |
| #22558967 | 2 |
| #22558891 | 2 |
| #22558890 | 2 |
| M16×C67⋊C8 | 2 |
| C67×#1997 | 2 |
| #9798 | 67 |