Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
368 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 91 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. C2×#10587479 | C2 | semidirect |
| 2. C2×#10587503 | C2 | semidirect |
| 3. C2×#10587503 | C2 | semidirect |
| 4. C2×C22⋊#3622 | C2 | semidirect |
| 5. #11762669 | C2 | semidirect |
| 6. #11762571 | C2 | semidirect |
| 60. C2×#3622 | D4 | semidirect |
| 168. C17 | #2034 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587479 | 2 |
| C2×#10587503 | 2 |
| C2×C22⋊#3622 | 2 |
| #11762669 | 2 |
| #11762571 | 2 |
| C2×C17×#121 | 2 |
| #2034 | 17 |