Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
376 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 78 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×#10587533 | C2 | semidirect |
| 2. C2×#10587547 | C2 | semidirect |
| 3. C2×#10587532 | C2 | semidirect |
| 4. #11763761 | C2 | semidirect |
| 11. C2×D8×C17 | C4 | semidirect |
| 12. C2×#63228 | C4 | semidirect |
| 15. C2×D136 | C4 | semidirect |
| 70. C8×C17 | C22⋊C4 | semidirect |
| 71. #3622 | C22⋊C4 | semidirect |
| 106. C2×D8 | #595 | semidirect |
| 115. C17 | #1972 | semidirect |
| 167. C8 | C22⋊#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587533 | 2 |
| C2×#10587547 | 2 |
| C2×#10587532 | 2 |
| #11763761 | 2 |
| C2×D8×D17 | 2 |
| #1972 | 17 |