Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
610 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 610 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 |
|---|---|---|
| 2. #22561049 | C2 | semidirect |
| 3. #22558967 | C2 | semidirect |
| 4. #22558878 | C2 | semidirect |
| 5. #22558877 | C2 | semidirect |
| 6. M16×C67⋊C8 | C2 | semidirect |
| 7. C67×#1965 | C2 | semidirect |
| 97. M16×C67 | D8 | semidirect |
| 142. C67⋊C8 | #100 | semidirect |
| 171. #1965 | D67 | semidirect |
| 176. C67 | #9802 | semidirect |
| 261. M16 | #11761613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863772 | 2 |
| #22561049 | 2 |
| #22558967 | 2 |
| #22558878 | 2 |
| #22558877 | 2 |
| M16×C67⋊C8 | 2 |
| C67×#1965 | 2 |
| #9802 | 67 |