Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
508 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 107 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×#16863517 | C2 | semidirect |
| 3. C2×#16863207 | C2 | semidirect |
| 4. #22561086 | C2 | semidirect |
| 5. #22558309 | C2 | semidirect |
| 6. #22558288 | C2 | semidirect |
| 7. C2×#361×C67 | C2 | semidirect |
| 12. C2×#14523987 | C4 | semidirect |
| 13. C2×#14523984 | C4 | semidirect |
| 79. Dic268 | C22⋊C4 | semidirect |
| 83. D536 | C22⋊C4 | semidirect |
| 180. C2×#361 | D67 | semidirect |
| 185. C67 | #13040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863832 | 2 |
| C2×#16863517 | 2 |
| C2×#16863207 | 2 |
| #22561086 | 2 |
| #22558309 | 2 |
| #22558288 | 2 |
| C2×#361×C67 | 2 |
| #13040 | 67 |