Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
690 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 113 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. #22571131 | C2 | semidirect |
| 2. C2×#16863768 | C2 | semidirect |
| 3. #22561198 | C2 | semidirect |
| 4. #22558877 | C2 | semidirect |
| 5. #22558660 | C2 | semidirect |
| 6. #22558047 | C2 | semidirect |
| 112. M16×C67 | SD16 | semidirect |
| 195. C67 | #10146 | semidirect |
| 292. M16 | #11761616 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571131 | 2 |
| C2×#16863768 | 2 |
| #22561198 | 2 |
| #22558877 | 2 |
| #22558660 | 2 |
| #22558047 | 2 |
| C67×#3151 | 2 |
| #10146 | 67 |