Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
306 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22562482 | C2 | semidirect |
| 3. #22562433 | C2 | semidirect |
| 4. #22559802 | C2 | semidirect |
| 5. #22559798 | C2 | semidirect |
| 6. C16×C67⋊C8 | C2 | semidirect |
| 7. C67×#2240 | C2 | semidirect |
| 57. C67⋊C16 | SD16 | semidirect |
| 90. C67⋊C8 | D16 | semidirect |
| 113. #2240 | D67 | semidirect |
| 117. C67 | #12503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562482 | 2 |
| #22562458 | 2 |
| #22562433 | 2 |
| #22559802 | 2 |
| #22559798 | 2 |
| C16×C67⋊C8 | 2 |
| C67×#2240 | 2 |
| #12503 | 67 |