Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
564 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 1. #22570948 | C2 | semidirect |
| 2. #22569114 | C2 | semidirect |
| 3. #22562425 | C2 | semidirect |
| 4. #22562377 | C2 | semidirect |
| 5. #22562286 | C2 | semidirect |
| 6. #22562285 | C2 | semidirect |
| 7. #22562156 | C2 | semidirect |
| 8. #22562106 | C2 | semidirect |
| 9. #22562104 | C2 | semidirect |
| 10. #22562020 | C2 | semidirect |
| 11. C67×#2230 | C2 | semidirect |
| 17. #16863773 | C22 | semidirect |
| 27. #16863507 | C22 | semidirect |
| 31. #16863218 | C22 | semidirect |
| 32. #16863217 | C22 | semidirect |
| 33. #16863210 | C22 | semidirect |
| 34. #16863208 | C22 | semidirect |
| 37. #16863173 | C22 | semidirect |
| 38. #498×C67 | C22 | semidirect |
| 40. #365×C67 | C22 | semidirect |
| 41. #364×C67 | C22 | semidirect |
| 111. Dic268 | #41 | semidirect |
| 120. D536 | #41 | semidirect |
| 144. Q16×C67 | #41 | semidirect |
| 146. D8×C67 | #41 | semidirect |
| 225. #2230 | D67 | semidirect |
| 232. C67 | #33688 | semidirect |
| 238. #498 | C2×D67 | semidirect |
| 255. #365 | C2×D67 | semidirect |
| 257. #364 | C2×D67 | semidirect |
| 336. Q16 | #11761629 | semidirect |
| 347. D8 | #11761629 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570948 | 2 |
| #22569114 | 2 |
| #22562425 | 2 |
| #22562377 | 2 |
| #22562286 | 2 |
| #22562285 | 2 |
| #22562156 | 2 |
| #22562106 | 2 |
| #22562104 | 2 |
| #22562020 | 2 |
| C67×#2230 | 2 |
| #33688 | 67 |