Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
372 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22562445 | C2 | semidirect |
| 2. #22562356 | C2 | semidirect |
| 3. #22559722 | C2 | semidirect |
| 4. #22558252 | C2 | semidirect |
| 5. #22558176 | C2 | semidirect |
| 6. #22558167 | C2 | semidirect |
| 8. #16863801 | C22 | semidirect |
| 11. C4⋊(C67⋊C16) | C22 | semidirect |
| 15. #16863172 | C22 | semidirect |
| 16. #16863147 | C22 | semidirect |
| 91. D8×C67 | SD16 | semidirect |
| 174. C67 | #12378 | semidirect |
| 253. D8 | #11761616 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562445 | 2 |
| #22562356 | 2 |
| #22559722 | 2 |
| #22558252 | 2 |
| #22558176 | 2 |
| #22558167 | 2 |
| C67×#3273 | 2 |
| #12378 | 67 |