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. #22570945 | C2 | semidirect |
| 2. #22569114 | C2 | semidirect |
| 3. #22562422 | C2 | semidirect |
| 4. #22562381 | C2 | semidirect |
| 5. #22562380 | C2 | semidirect |
| 6. #22562282 | C2 | semidirect |
| 7. #22562153 | C2 | semidirect |
| 8. #22562110 | C2 | semidirect |
| 9. #22562108 | C2 | semidirect |
| 10. #22562020 | C2 | semidirect |
| 11. C67×#2213 | C2 | semidirect |
| 16. #16863794 | C22 | semidirect |
| 26. #16863508 | C22 | semidirect |
| 30. #16863220 | C22 | semidirect |
| 31. #16863219 | C22 | semidirect |
| 32. #16863217 | C22 | semidirect |
| 33. #16863209 | C22 | semidirect |
| 37. #16863173 | C22 | semidirect |
| 39. #493×C67 | C22 | semidirect |
| 41. #364×C67 | C22 | semidirect |
| 42. #361×C67 | C22 | semidirect |
| 109. Dic268 | #41 | semidirect |
| 114. D536 | #41 | semidirect |
| 142. Q16×C67 | #41 | semidirect |
| 148. D8×C67 | #41 | semidirect |
| 227. #2213 | D67 | semidirect |
| 232. C67 | #33688 | semidirect |
| 239. #493 | C2×D67 | semidirect |
| 257. #364 | C2×D67 | semidirect |
| 259. #361 | C2×D67 | semidirect |
| 336. Q16 | #11761627 | semidirect |
| 347. D8 | #11761627 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570945 | 2 |
| #22569114 | 2 |
| #22562422 | 2 |
| #22562381 | 2 |
| #22562380 | 2 |
| #22562282 | 2 |
| #22562153 | 2 |
| #22562110 | 2 |
| #22562108 | 2 |
| #22562020 | 2 |
| C67×#2213 | 2 |
| #33688 | 67 |