Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
536 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 95 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×#16863837 | C2 | semidirect |
| 3. #22570698 | C2 | semidirect |
| 4. #22561944 | C2 | semidirect |
| 5. #22561105 | C2 | semidirect |
| 6. #22558294 | C2 | semidirect |
| 7. C67×#2141 | C2 | semidirect |
| 216. #2141 | D67 | semidirect |
| 219. C67 | #13335 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573345 | 2 |
| C2×#16863837 | 2 |
| #22570698 | 2 |
| #22561944 | 2 |
| #22561105 | 2 |
| #22558294 | 2 |
| C67×#2141 | 2 |
| #13335 | 67 |