Finite Group DatabasebetaFinite Group DatabasebetaOrder 17216.
134 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 56 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×D269⋊C8 | C2 | semidirect |
| 2. C22×#14524137 | C2 | semidirect |
| 3. #22575520 | C2 | semidirect |
| 4. #22575510 | C2 | semidirect |
| 5. C22⋊#14524137 | C2 | semidirect |
| 6. C4×#14524137 | C2 | semidirect |
| 24. #14524137 | D4 | semidirect |
| 26. C22⋊D269 | C8 | semidirect |
| 39. C22×C269 | C2×C8 | semidirect |
| 43. C2×D269 | C2×C8 | semidirect |
| 47. Dic269 | C2×C8 | semidirect |
| 55. C269 | C8×D4 | semidirect |
| 98. C22 | D269⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D269⋊C8 | 2 |
| C22×#14524137 | 2 |
| #22575520 | 2 |
| #22575510 | 2 |
| C22⋊#14524137 | 2 |
| C4×#14524137 | 2 |
| #22575413 | 2 |
| C8×D4 | 269 |