Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
332 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 67 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. #22558383 | C2 | semidirect |
| 4. #22558368 | C2 | semidirect |
| 6. #16864008 | C4 | semidirect |
| 8. #16863768 | C4 | semidirect |
| 9. #16863760 | C4 | semidirect |
| 15. #16863457 | C4 | semidirect |
| 28. #14524043 | C2×C4 | semidirect |
| 30. #14524035 | C2×C4 | semidirect |
| 42. #14523954 | C2×C4 | semidirect |
| 43. C4×C67⋊C8 | C2×C4 | semidirect |
| 158. C67 | #13607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571281 | 2 |
| #22561901 | 2 |
| #22558383 | 2 |
| #22558368 | 2 |
| C67×#2127 | 2 |
| #13607 | 67 |