Finite Group DatabasebetaFinite Group DatabasebetaOrder 17216.
210 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 50 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. C2×C22⋊#11761640 | C2 | semidirect |
| 2. #22575512 | C2 | semidirect |
| 3. #22575511 | C2 | semidirect |
| 7. C22⋊#11761640 | C22 | semidirect |
| 8. C23×D269 | C4 | semidirect |
| 11. C2×C22⋊D269 | C4 | semidirect |
| 15. C2×C4×D269 | C4 | semidirect |
| 16. C2×D4×C269 | C4 | semidirect |
| 24. C22×D269 | C2×C4 | semidirect |
| 31. C2×Dic269 | C2×C4 | semidirect |
| 35. C23×C269 | C2×C4 | semidirect |
| 37. C2×C4×C269 | C2×C4 | semidirect |
| 64. D269 | #99 | semidirect |
| 65. C269 | C2×#99 | semidirect |
| 78. C2×D4 | #11761640 | semidirect |
| 93. C23 | C2×#11761640 | semidirect |
| 103. C2×C4 | C2×#11761640 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#11761640 | 2 |
| #22575512 | 2 |
| #22575511 | 2 |
| C2×D4×D269 | 2 |
| C2×#99 | 269 |