Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
312 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22573077 | C2 | semidirect |
| 2. #22562432 | C2 | semidirect |
| 4. #22558268 | C2 | semidirect |
| 5. Q8⋊(C67⋊C16) | C2 | semidirect |
| 6. #22558169 | C2 | semidirect |
| 7. C67×#1668 | C2 | semidirect |
| 58. D536 | SD16 | semidirect |
| 136. #1668 | D67 | semidirect |
| 140. C67 | #12355 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573077 | 2 |
| #22562432 | 2 |
| #22562241 | 2 |
| #22558268 | 2 |
| Q8⋊(C67⋊C16) | 2 |
| #22558169 | 2 |
| C67×#1668 | 2 |
| #12355 | 67 |