Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
490 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 3. #22561182 | C2 | semidirect |
| 4. #22558893 | C2 | semidirect |
| 6. #22558068 | C2 | semidirect |
| 7. C67×#1275 | C2 | semidirect |
| 11. #16863769 | C4 | semidirect |
| 12. #16863747 | C4 | semidirect |
| 107. C2×C8×C67 | SD16 | semidirect |
| 181. #1275 | D67 | semidirect |
| 182. C67 | #9289 | semidirect |
| 272. C2×C8 | #11761617 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571136 | 2 |
| #22568928 | 2 |
| #22561182 | 2 |
| #22558893 | 2 |
| #22558770 | 2 |
| #22558068 | 2 |
| C67×#1275 | 2 |
| #9289 | 67 |