Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
348 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 3. C2×#10587486 | C2 | semidirect |
| 4. C2×C4×#3622 | C2 | semidirect |
| 6. #11762563 | C2 | semidirect |
| 7. C17×#336 | C2 | semidirect |
| 18. C2×#63218 | C4 | semidirect |
| 20. #10587491 | C4 | semidirect |
| 60. C2×C4×C17 | M16 | semidirect |
| 80. #3622 | C22⋊C4 | semidirect |
| 105. #336 | D17 | semidirect |
| 127. C17 | #1753 | semidirect |
| 175. C2×C4 | #63218 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63218 | 2 |
| C2×#10587491 | 2 |
| C2×#10587486 | 2 |
| C2×C4×#3622 | 2 |
| C4×#63227 | 2 |
| #11762563 | 2 |
| C17×#336 | 2 |
| #1753 | 17 |