Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
492 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22561153 | C2 | semidirect |
| 4. #22558761 | C2 | semidirect |
| 5. #22558074 | C2 | semidirect |
| 6. #22558066 | C2 | semidirect |
| 9. #16863791 | C4 | semidirect |
| 10. #16863755 | C4 | semidirect |
| 34. #14524043 | C2×C4 | semidirect |
| 35. #14524043 | C2×C4 | semidirect |
| 54. #14523954 | C2×C4 | semidirect |
| 212. C67 | #9379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571212 | 2 |
| #22563024 | 2 |
| #22561153 | 2 |
| #22558761 | 2 |
| #22558074 | 2 |
| #22558066 | 2 |
| C67×#1527 | 2 |
| #9379 | 67 |