Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
488 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 213 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. #11762865 | C2 | direct (N × H) |
| 3. C2×C4⋊#3622 | C2 | semidirect |
| 5. C2×#10587486 | C2 | semidirect |
| 6. C2×C17×C4⋊C8 | C2 | semidirect |
| 18. C17×C4⋊C8 | C22 | semidirect |
| 20. #10587486 | C22 | semidirect |
| 21. C4⋊#3622 | C22 | semidirect |
| 93. C2×C4⋊C8 | D17 | semidirect |
| 96. C2×C17 | #432 | semidirect |
| 113. C4⋊C8 | C2×D17 | semidirect |
| 116. C17 | C2×#432 | semidirect |
| 185. C2 | #11762865 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×D17 | 2 |
| #11762865 | 2 |
| C2×C4⋊#3622 | 2 |
| C2×#10587491 | 2 |
| C2×#10587486 | 2 |
| C2×C17×C4⋊C8 | 2 |
| C2×#432 | 17 |