Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
534 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22561023 | C2 | semidirect |
| 3. #22560375 | C2 | semidirect |
| 4. C2×#16863136 | C2 | semidirect |
| 5. C2×#16863135 | C2 | semidirect |
| 6. #22558091 | C2 | semidirect |
| 7. C67×#1959 | C2 | semidirect |
| 54. #14523954 | D4 | semidirect |
| 240. #1959 | D67 | semidirect |
| 245. C67 | #10424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568254 | 2 |
| #22561023 | 2 |
| #22560375 | 2 |
| C2×#16863136 | 2 |
| C2×#16863135 | 2 |
| #22558091 | 2 |
| C67×#1959 | 2 |
| #10424 | 67 |