Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
574 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 3. C2×#16863746 | C2 | semidirect |
| 4. #22558882 | C2 | semidirect |
| 6. #22558047 | C2 | semidirect |
| 7. C67×#1997 | C2 | semidirect |
| 107. M16×C67 | SD16 | semidirect |
| 177. #1997 | D67 | semidirect |
| 181. C67 | #10170 | semidirect |
| 270. M16 | #11761615 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571134 | 2 |
| #22570668 | 2 |
| C2×#16863746 | 2 |
| #22558882 | 2 |
| #22558659 | 2 |
| #22558047 | 2 |
| C67×#1997 | 2 |
| #10170 | 67 |