Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
184 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 81 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. #22562504 | C2 | semidirect |
| 2. #22562503 | C2 | semidirect |
| 4. #22558406 | C2 | semidirect |
| 5. #22558350 | C2 | semidirect |
| 6. #22558342 | C2 | semidirect |
| 7. C67×#1401 | C2 | semidirect |
| 97. #1401 | D67 | semidirect |
| 99. C67 | #13648 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562504 | 2 |
| #22562503 | 2 |
| #22562044 | 2 |
| #22558406 | 2 |
| #22558350 | 2 |
| #22558342 | 2 |
| C67×#1401 | 2 |
| #13648 | 67 |