Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
174 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 37 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 |
|---|---|---|
| 4. #16863445 | C4 | semidirect |
| 8. #16863153 | C4 | semidirect |
| 81. C67 | #7438 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561762 | 2 |
| #22558330 | 2 |
| C67×#1315 | 2 |
| #7438 | 67 |