Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
188 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 51 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. C2×#16863231 | C2 | semidirect |
| 2. #22562504 | C2 | semidirect |
| 3. #22562330 | C2 | semidirect |
| 4. #22562326 | C2 | semidirect |
| 5. #22558412 | C2 | semidirect |
| 6. #22558400 | C2 | semidirect |
| 7. C67×#1419 | C2 | semidirect |
| 100. #1419 | D67 | semidirect |
| 101. C67 | #13700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863231 | 2 |
| #22562504 | 2 |
| #22562330 | 2 |
| #22562326 | 2 |
| #22558412 | 2 |
| #22558400 | 2 |
| C67×#1419 | 2 |
| #13700 | 67 |