Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
802 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 802 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22563037 | C2 | semidirect |
| 3. #22561044 | C2 | semidirect |
| 4. #22560152 | C2 | semidirect |
| 5. #22558726 | C2 | semidirect |
| 6. #22558094 | C2 | semidirect |
| 7. C67×#1305 | C2 | semidirect |
| 9. C2×#14524071 | C4 | semidirect |
| 16. #16863398 | C4 | semidirect |
| 35. C22×D268 | C2×C4 | semidirect |
| 49. C2×C4⋊Dic67 | C2×C4 | semidirect |
| 67. C2×M16×C67 | C2×C4 | semidirect |
| 188. D268 | #99 | semidirect |
| 244. #1305 | D67 | semidirect |
| 246. C67 | #9365 | semidirect |
| 285. C2×M16 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569463 | 2 |
| #22563037 | 2 |
| #22561044 | 2 |
| #22560152 | 2 |
| #22558726 | 2 |
| #22558094 | 2 |
| C67×#1305 | 2 |
| #9365 | 67 |