Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
484 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 105 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. C4×#14524065 | C2 | semidirect |
| 3. #22561945 | C2 | semidirect |
| 4. #22561936 | C2 | semidirect |
| 5. #22558323 | C2 | semidirect |
| 6. #22558291 | C2 | semidirect |
| 7. C67×#1974 | C2 | semidirect |
| 10. #16863837 | C4 | semidirect |
| 12. #16863832 | C4 | semidirect |
| 50. #14523983 | C2×C4 | semidirect |
| 62. C2×Q16×C67 | C2×C4 | semidirect |
| 64. C2×D8×C67 | C2×C4 | semidirect |
| 196. #1974 | D67 | semidirect |
| 199. C67 | #13027 | semidirect |
| 232. C2×Q16 | C4×D67 | semidirect |
| 236. C2×D8 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573343 | 2 |
| C4×#14524065 | 2 |
| #22561945 | 2 |
| #22561936 | 2 |
| #22558323 | 2 |
| #22558291 | 2 |
| C67×#1974 | 2 |
| #13027 | 67 |