Finite Group DatabasebetaFinite Group DatabasebetaOrder 17216.
134 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 45 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×#16864387 | C2 | semidirect |
| 2. C22×#14524130 | C2 | semidirect |
| 3. #22575427 | C2 | semidirect |
| 4. #22575386 | C2 | semidirect |
| 5. #22575374 | C2 | semidirect |
| 6. #22575373 | C2 | semidirect |
| 7. #121×C269 | C2 | semidirect |
| 27. #14524130 | D4 | semidirect |
| 43. C22×C269 | D8 | semidirect |
| 59. C269 | #466 | semidirect |
| 64. #121 | D269 | semidirect |
| 106. C22 | #16864387 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16864387 | 2 |
| C22×#14524130 | 2 |
| #22575427 | 2 |
| #22575386 | 2 |
| #22575374 | 2 |
| #22575373 | 2 |
| #121×C269 | 2 |
| #466 | 269 |