Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
170 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 51 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×#10587471 | C2 | semidirect |
| 3. #11763193 | C2 | semidirect |
| 4. C4×D136 | C2 | semidirect |
| 5. #11762614 | C2 | semidirect |
| 6. #11762611 | C2 | semidirect |
| 7. C17×C4⋊C16 | C2 | semidirect |
| 76. C4⋊C16 | D17 | semidirect |
| 97. C17 | #2210 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587471 | 2 |
| C2×D272 | 2 |
| #11763193 | 2 |
| C4×D136 | 2 |
| #11762614 | 2 |
| #11762611 | 2 |
| C17×C4⋊C16 | 2 |
| #2210 | 17 |