Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
402 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 402 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 |
|---|---|---|
| 3. #22558368 | C2 | semidirect |
| 7. C2×#14524043 | C4 | semidirect |
| 8. #16863791 | C4 | semidirect |
| 13. C4×#11761612 | C4 | semidirect |
| 153. C67 | #13580 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570669 | 2 |
| #22561894 | 2 |
| #22558368 | 2 |
| C67×#2126 | 2 |
| #13580 | 67 |