Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
554 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 139 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. #22561037 | C2 | semidirect |
| 3. #22558968 | C2 | semidirect |
| 4. #22558661 | C2 | semidirect |
| 5. C42×C8×C67 | C2 | semidirect |
| 7. #16863801 | C4 | semidirect |
| 8. #16863773 | C4 | semidirect |
| 9. #16863743 | C4 | semidirect |
| 74. C42×C67 | D8 | semidirect |
| 104. C8×C67 | #104 | semidirect |
| 130. C42×C8 | D67 | semidirect |
| 133. C67 | #9844 | semidirect |
| 202. C42 | D536 | semidirect |
| 233. C8 | #14523971 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570788 | 2 |
| #22561037 | 2 |
| #22558968 | 2 |
| #22558661 | 2 |
| C42×C8×C67 | 2 |
| #9844 | 67 |