Finite Group DatabasebetaFinite Group DatabasebetaOrder 17216.
280 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 115 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. C22×Dic538 | C2 | semidirect |
| 2. C2×Q8×D269 | C2 | semidirect |
| 3. #22575452 | C2 | semidirect |
| 4. #22575451 | C2 | semidirect |
| 5. #22575433 | C2 | semidirect |
| 6. #22575431 | C2 | semidirect |
| 7. #22575430 | C2 | semidirect |
| 8. #22575418 | C2 | semidirect |
| 11. C22⋊Q8×C269 | C2 | semidirect |
| 41. Dic538 | D4 | semidirect |
| 42. C22⋊D269 | Q8 | semidirect |
| 60. C22×C269 | C2×Q8 | semidirect |
| 64. C2×D269 | C2×Q8 | semidirect |
| 73. Dic269 | C2×Q8 | semidirect |
| 79. C269 | D4×Q8 | semidirect |
| 88. C22⋊Q8 | D269 | semidirect |
| 143. C22 | Q8×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic538 | 2 |
| C2×Q8×D269 | 2 |
| #22575452 | 2 |
| #22575451 | 2 |
| #22575433 | 2 |
| #22575431 | 2 |
| #22575430 | 2 |
| #22575418 | 2 |
| C4×C22⋊D269 | 2 |
| #22575413 | 2 |
| C22⋊Q8×C269 | 2 |
| D4×Q8 | 269 |