Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
170 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 49 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×#10587469 | C2 | semidirect |
| 3. #11763046 | C2 | semidirect |
| 4. #11762609 | C2 | semidirect |
| 5. C17×#367 | C2 | semidirect |
| 26. C16×C17 | D4 | semidirect |
| 55. #367 | D17 | semidirect |
| 70. C17 | #2218 | semidirect |
| 83. C16 | D68 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D272 | 2 |
| C2×#10587469 | 2 |
| #11763046 | 2 |
| #11762609 | 2 |
| C17×#367 | 2 |
| #2218 | 17 |