Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
478 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 75 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. #11763373 | C2 | semidirect |
| 2. C2×#10587626 | C2 | semidirect |
| 3. C2×#10587508 | C2 | semidirect |
| 4. #11762814 | C2 | semidirect |
| 5. C2×#10587494 | C2 | semidirect |
| 6. #11762570 | C2 | semidirect |
| 7. C2×C17×AGL(1,ℤ/8) | C2 | semidirect |
| 35. C2×Q8×C17 | D4 | semidirect |
| 42. C2×D4×C17 | D4 | semidirect |
| 43. C2×D4×C17 | D4 | semidirect |
| 59. M16×C17 | D4 | semidirect |
| 63. C4⋊Dic17 | D4 | semidirect |
| 66. C4×Dic17 | D4 | semidirect |
| 132. C2×AGL(1,ℤ/8) | D17 | semidirect |
| 167. C17 | #2002 | semidirect |
| 174. C2×Q8 | C22⋊D17 | semidirect |
| 190. C2×D4 | C22⋊D17 | semidirect |
| 191. C2×D4 | C22⋊D17 | semidirect |
| 200. M16 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763373 | 2 |
| C2×#10587626 | 2 |
| C2×#10587508 | 2 |
| #11762814 | 2 |
| C2×#10587494 | 2 |
| #11762570 | 2 |
| C2×C17×AGL(1,ℤ/8) | 2 |
| #2002 | 17 |