Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
216 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 57 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×D272 | C2 | semidirect |
| 2. C2×#10587497 | C2 | semidirect |
| 3. #11763184 | C2 | semidirect |
| 4. C16×Dic17 | C2 | semidirect |
| 5. C2×C17×D16 | C2 | semidirect |
| 27. C16×C17 | D4 | semidirect |
| 28. #63214 | D4 | semidirect |
| 49. Dic17 | D16 | semidirect |
| 52. C2×D16 | D17 | semidirect |
| 69. C17 | #2246 | semidirect |
| 82. C16 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D272 | 2 |
| C2×#10587497 | 2 |
| #11763184 | 2 |
| C16×Dic17 | 2 |
| C2×C17×D16 | 2 |
| #2246 | 17 |