Finite Group DatabasebetaFinite Group DatabasebetaOrder 17216.
162 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 43 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×#16864401 | C2 | semidirect |
| 2. C2×#16864391 | C2 | semidirect |
| 3. C2×#16864387 | C2 | semidirect |
| 4. #22575428 | C2 | semidirect |
| 5. #22575376 | C2 | semidirect |
| 6. #22575365 | C2 | semidirect |
| 7. #102×C269 | C2 | semidirect |
| 26. Dic538 | D4 | semidirect |
| 39. D4×C269 | D4 | semidirect |
| 64. C269 | #449 | semidirect |
| 71. #102 | D269 | semidirect |
| 98. D4 | D1076 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16864401 | 2 |
| C2×#16864391 | 2 |
| C2×#16864387 | 2 |
| #22575428 | 2 |
| #22575376 | 2 |
| #22575365 | 2 |
| #102×C269 | 2 |
| #449 | 269 |