Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
348 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 75 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. #22562020 | C2 | semidirect |
| 3. #22558503 | C2 | semidirect |
| 4. #22558185 | C2 | semidirect |
| 5. #22558184 | C2 | semidirect |
| 6. #22558183 | C2 | semidirect |
| 7. C67×#1335 | C2 | semidirect |
| 19. #16863217 | C22 | semidirect |
| 23. #16863117 | C22 | semidirect |
| 25. #364×C67 | C22 | semidirect |
| 26. C82×C67 | C22 | semidirect |
| 172. #1335 | D67 | semidirect |
| 173. C67 | #11670 | semidirect |
| 187. #364 | C2×D67 | semidirect |
| 192. C82 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569114 | 2 |
| #22562020 | 2 |
| #22558503 | 2 |
| #22558185 | 2 |
| #22558184 | 2 |
| #22558183 | 2 |
| C67×#1335 | 2 |
| #11670 | 67 |