Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
408 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 2. C2×#16863221 | C2 | semidirect |
| 3. C2×#16863202 | C2 | semidirect |
| 4. #22561919 | C2 | semidirect |
| 5. C2×#16863180 | C2 | semidirect |
| 6. #22558319 | C2 | semidirect |
| 7. C67×#1816 | C2 | semidirect |
| 46. C2×C67⋊C16 | D4 | semidirect |
| 189. #1816 | D67 | semidirect |
| 191. C67 | #13384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569879 | 2 |
| C2×#16863221 | 2 |
| C2×#16863202 | 2 |
| #22561919 | 2 |
| C2×#16863180 | 2 |
| #22558319 | 2 |
| C67×#1816 | 2 |
| #13384 | 67 |