Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
154 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 2. #11762922 | C2 | semidirect |
| 3. #11762633 | C2 | semidirect |
| 4. #11762621 | C2 | semidirect |
| 5. #11762619 | C2 | semidirect |
| 6. #11762587 | C2 | semidirect |
| 7. C17×#444 | C2 | semidirect |
| 15. #10587499 | C4 | semidirect |
| 16. #10587497 | C4 | semidirect |
| 24. Q16×C17 | C2×C4 | semidirect |
| 26. D8×C17 | C2×C4 | semidirect |
| 38. #63214 | C2×C4 | semidirect |
| 66. #444 | D17 | semidirect |
| 89. C17 | AGL(1,ℤ/16) | semidirect |
| 93. Q16 | C4×D17 | semidirect |
| 97. D8 | C4×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763244 | 2 |
| #11762922 | 2 |
| #11762633 | 2 |
| #11762621 | 2 |
| #11762619 | 2 |
| #11762587 | 2 |
| C17×#444 | 2 |
| AGL(1,ℤ/16) | 17 |