Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
480 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22560205 | C2 | semidirect |
| 4. #22558335 | C2 | semidirect |
| 5. C67×#1801 | C2 | semidirect |
| 191. #1801 | D67 | semidirect |
| 193. C67 | #12803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562916 | 2 |
| C2×#16863192 | 2 |
| #22560205 | 2 |
| #22558335 | 2 |
| C67×#1801 | 2 |
| #12803 | 67 |