Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
370 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 97 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. #11763292 | C2 | semidirect |
| 2. C2×#10587508 | C2 | semidirect |
| 3. #11762814 | C2 | semidirect |
| 4. #11762712 | C2 | semidirect |
| 5. #11762577 | C2 | semidirect |
| 6. #11762570 | C2 | semidirect |
| 11. C17×AGL(1,ℤ/8) | C4 | semidirect |
| 40. C2×D4×C17 | C2×C4 | semidirect |
| 50. M16×C17 | C2×C4 | semidirect |
| 75. Q8×C17 | C22⋊C4 | semidirect |
| 83. D4×C17 | C22⋊C4 | semidirect |
| 143. AGL(1,ℤ/8) | Dic17 | semidirect |
| 160. C17 | #1883 | semidirect |
| 173. C2×D4 | C2×Dic17 | semidirect |
| 185. M16 | C2×Dic17 | semidirect |
| 208. Q8 | C22⋊Dic17 | semidirect |
| 216. D4 | C22⋊Dic17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763292 | 2 |
| C2×#10587508 | 2 |
| #11762814 | 2 |
| #11762712 | 2 |
| #11762577 | 2 |
| #11762570 | 2 |
| C2×C17×AGL(1,ℤ/8) | 2 |
| #1883 | 17 |