Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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. Q8×D68 | C2 | semidirect |
| 3. #11763161 | C2 | semidirect |
| 4. #11763141 | C2 | semidirect |
| 5. #11763039 | C2 | semidirect |
| 6. #11763015 | C2 | semidirect |
| 7. #11762949 | C2 | semidirect |
| 8. C4×#63230 | C2 | semidirect |
| 9. #11762874 | C2 | semidirect |
| 10. #103×D17 | C2 | semidirect |
| 11. C17×#475 | C2 | semidirect |
| 81. Q8×C17 | #41 | semidirect |
| 94. D68 | SD16 | semidirect |
| 128. #475 | D17 | semidirect |
| 169. C17 | #3298 | semidirect |
| 213. Q8 | #63256 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D68 | 2 |
| #11763462 | 2 |
| #11763161 | 2 |
| #11763141 | 2 |
| #11763039 | 2 |
| #11763015 | 2 |
| #11762949 | 2 |
| C4×#63230 | 2 |
| #11762874 | 2 |
| #103×D17 | 2 |
| C17×#475 | 2 |
| #3298 | 17 |