Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
512 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 141 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×#10587556 | C2 | semidirect |
| 2. #11762745 | C2 | semidirect |
| 3. #11762740 | C2 | semidirect |
| 4. #11762734 | C2 | semidirect |
| 6. #11762682 | C2 | semidirect |
| 7. #11762677 | C2 | semidirect |
| 121. C17 | #2633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587556 | 2 |
| #11762745 | 2 |
| #11762740 | 2 |
| #11762734 | 2 |
| #11762723 | 2 |
| #11762682 | 2 |
| #11762677 | 2 |
| C2×C4×D4×C17 | 2 |
| #2633 | 17 |