Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
230 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 85 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. #11762866 | C2 | semidirect |
| 2. C2×C4×#3622 | C2 | semidirect |
| 3. Q8⋊#3622 | C2 | semidirect |
| 4. D4⋊#3622 | C2 | semidirect |
| 113. C17 | #1494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11762866 | 2 |
| C2×C4×#3622 | 2 |
| Q8⋊#3622 | 2 |
| D4⋊#3622 | 2 |
| C17×#529 | 2 |
| #1494 | 17 |