Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
380 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 99 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. #364×D67 | C2 | semidirect |
| 3. #22558491 | C2 | semidirect |
| 4. #22558183 | C2 | semidirect |
| 5. #22558182 | C2 | semidirect |
| 6. #22558181 | C2 | semidirect |
| 7. C67×#1335 | C2 | semidirect |
| 20. #16863217 | C22 | semidirect |
| 23. C8×C67⋊C8 | C22 | semidirect |
| 25. #364×C67 | C22 | semidirect |
| 26. C82×C67 | C22 | semidirect |
| 28. #14524066 | C8 | semidirect |
| 32. #14524062 | C8 | semidirect |
| 33. Q16×D67 | C8 | semidirect |
| 35. D8×D67 | C8 | semidirect |
| 187. #1335 | D67 | semidirect |
| 188. C67 | #11602 | semidirect |
| 204. #364 | C2×D67 | semidirect |
| 207. C82 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #443×D67 | 2 |
| #364×D67 | 2 |
| #22558491 | 2 |
| #22558183 | 2 |
| #22558182 | 2 |
| #22558181 | 2 |
| C67×#1335 | 2 |
| #11602 | 67 |