Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
224 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 74 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. #11763865 | C2 | semidirect |
| 2. C2×#10587529 | C2 | semidirect |
| 3. #11763708 | C2 | semidirect |
| 4. #11763707 | C2 | semidirect |
| 17. #10587538 | C22 | semidirect |
| 18. C2×#63216 | C22 | semidirect |
| 107. D17 | #350 | semidirect |
| 125. C17 | C2×#350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763865 | 2 |
| C2×#10587529 | 2 |
| #11763708 | 2 |
| #11763707 | 2 |
| #131×D17 | 2 |
| C2×#350 | 17 |