Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
444 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 93 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×#10587632 | C2 | semidirect |
| 3. C2×#10587506 | C2 | semidirect |
| 4. C2×#10587503 | C2 | semidirect |
| 5. C2×#10587491 | C2 | semidirect |
| 6. #11762572 | C2 | semidirect |
| 7. C22×SD16×C17 | C2 | semidirect |
| 36. C2×Q8×C17 | D4 | semidirect |
| 60. C2×C8×C17 | D4 | semidirect |
| 66. C4⋊Dic17 | D4 | semidirect |
| 85. C22×D17 | SD16 | semidirect |
| 149. C22×SD16 | D17 | semidirect |
| 186. C17 | #2000 | semidirect |
| 194. C2×Q8 | C22⋊D17 | semidirect |
| 221. C2×C8 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587632 | 2 |
| C2×#10587624 | 2 |
| C2×#10587506 | 2 |
| C2×#10587503 | 2 |
| C2×#10587491 | 2 |
| #11762572 | 2 |
| C22×SD16×C17 | 2 |
| #2000 | 17 |