Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
286 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 68 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. #11763820 | C2 | semidirect |
| 4. #11763753 | C2 | semidirect |
| 5. #11763688 | C2 | semidirect |
| 6. #11763680 | C2 | semidirect |
| 25. C17×#104 | C4 | semidirect |
| 26. #10587508 | C4 | semidirect |
| 27. #10587496 | C4 | semidirect |
| 28. #10587476 | C4 | semidirect |
| 58. M16×C17 | C2×C4 | semidirect |
| 59. C42×C17 | C2×C4 | semidirect |
| 61. C4×Dic17 | C2×C4 | semidirect |
| 62. #63223 | C2×C4 | semidirect |
| 155. #104 | #595 | semidirect |
| 159. C17 | #1860 | semidirect |
| 179. M16 | C2×#595 | semidirect |
| 195. C42 | C2×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763878 | 2 |
| #11763820 | 2 |
| #11763800 | 2 |
| #11763753 | 2 |
| #11763688 | 2 |
| #11763680 | 2 |
| #104×D17 | 2 |
| #1860 | 17 |