Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 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×#10587590 | C2 | semidirect |
| 2. C2×#10587587 | C2 | semidirect |
| 3. #11763390 | C2 | semidirect |
| 4. #11763068 | C2 | semidirect |
| 5. #11763063 | C2 | semidirect |
| 6. #11763039 | C2 | semidirect |
| 7. #11762808 | C2 | semidirect |
| 8. C2×C17×#106 | C2 | semidirect |
| 45. C2×C8×C17 | D4 | semidirect |
| 107. C2×#106 | D17 | semidirect |
| 135. C17 | #3060 | semidirect |
| 158. C2×C8 | D68 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587590 | 2 |
| C2×#10587587 | 2 |
| #11763390 | 2 |
| #11763068 | 2 |
| #11763063 | 2 |
| #11763039 | 2 |
| #11762808 | 2 |
| C2×C17×#106 | 2 |
| #3060 | 17 |