Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
342 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22558301 | C2 | semidirect |
| 4. #22558300 | C2 | semidirect |
| 5. C2×#366×C67 | C2 | semidirect |
| 107. C2×#366 | D67 | semidirect |
| 112. C67 | #13492 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×(C2×D67)⋊C16 | 2 |
| #22560235 | 2 |
| #22558301 | 2 |
| #22558300 | 2 |
| C2×#366×C67 | 2 |
| #13492 | 67 |