Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
484 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22568980 | C2 | semidirect |
| 3. #22561944 | C2 | semidirect |
| 4. #22561936 | C2 | semidirect |
| 5. #22561095 | C2 | semidirect |
| 6. #22558290 | C2 | semidirect |
| 7. C67×#1389 | C2 | semidirect |
| 12. #16863839 | C4 | semidirect |
| 14. #16863834 | C4 | semidirect |
| 39. C2×Dic268 | C2×C4 | semidirect |
| 43. C2×D536 | C2×C4 | semidirect |
| 70. M32×C67 | C2×C4 | semidirect |
| 197. #1389 | D67 | semidirect |
| 199. C67 | #13027 | semidirect |
| 254. M32 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573345 | 2 |
| #22568980 | 2 |
| #22561944 | 2 |
| #22561936 | 2 |
| #22561095 | 2 |
| #22558290 | 2 |
| C67×#1389 | 2 |
| #13027 | 67 |