Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
470 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 4. #22558961 | C2 | semidirect |
| 5. #22558899 | C2 | semidirect |
| 6. #22558112 | C2 | semidirect |
| 7. C67×#1986 | C2 | semidirect |
| 101. M16×C67 | SD16 | semidirect |
| 192. #1986 | D67 | semidirect |
| 198. C67 | #10504 | semidirect |
| 287. M16 | #11761615 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571147 | 2 |
| #22561136 | 2 |
| #22561049 | 2 |
| #22558961 | 2 |
| #22558899 | 2 |
| #22558112 | 2 |
| C67×#1986 | 2 |
| #10504 | 67 |