Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
620 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 2. #22563117 | C2 | semidirect |
| 3. #22558768 | C2 | semidirect |
| 4. #22558705 | C2 | semidirect |
| 5. #22558599 | C2 | semidirect |
| 6. #22558110 | C2 | semidirect |
| 7. C67×#1286 | C2 | semidirect |
| 13. #16863602 | C4 | semidirect |
| 14. #16863592 | C4 | semidirect |
| 37. #14524043 | C2×C4 | semidirect |
| 38. #14524040 | C2×C4 | semidirect |
| 69. C4⋊C8×C67 | C2×C4 | semidirect |
| 221. #1286 | D67 | semidirect |
| 222. C67 | #9179 | semidirect |
| 277. C4⋊C8 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569675 | 2 |
| #22563117 | 2 |
| #22558768 | 2 |
| #22558705 | 2 |
| #22558599 | 2 |
| #22558110 | 2 |
| C67×#1286 | 2 |
| #9179 | 67 |