Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
384 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×#10587478 | C2 | semidirect |
| 3. C2×#10587503 | C2 | semidirect |
| 4. C2×#10587480 | C2 | semidirect |
| 5. C2×C4×#3622 | C2 | semidirect |
| 6. #11762711 | C2 | semidirect |
| 7. C17×#390 | C2 | semidirect |
| 15. C2×#63228 | C4 | semidirect |
| 76. C2×C4×C17 | D8 | semidirect |
| 90. #3622 | C22⋊C4 | semidirect |
| 120. #390 | D17 | semidirect |
| 144. C17 | #1970 | semidirect |
| 203. C2×C4 | #63228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63228 | 2 |
| C2×#10587478 | 2 |
| C2×#10587503 | 2 |
| C2×#10587480 | 2 |
| C2×C4×#3622 | 2 |
| #11762711 | 2 |
| C17×#390 | 2 |
| #1970 | 17 |