Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
380 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 1. #22562003 | C2 | semidirect |
| 4. #22560999 | C2 | semidirect |
| 5. #22558302 | C2 | semidirect |
| 6. #22558298 | C2 | semidirect |
| 14. #16863212 | C4 | semidirect |
| 15. #16863209 | C4 | semidirect |
| 149. C67 | #12942 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562003 | 2 |
| #22561958 | 2 |
| C2×#16863203 | 2 |
| #22560999 | 2 |
| #22558302 | 2 |
| #22558298 | 2 |
| C67×#2957 | 2 |
| #12942 | 67 |