Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
430 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11763481 | C2 | semidirect |
| 2. #11763462 | C2 | semidirect |
| 3. #11763157 | C2 | semidirect |
| 4. #11763129 | C2 | semidirect |
| 5. #11763063 | C2 | semidirect |
| 6. #11763005 | C2 | semidirect |
| 7. #11762957 | C2 | semidirect |
| 8. C4×#63230 | C2 | semidirect |
| 9. #11762886 | C2 | semidirect |
| 10. #11762809 | C2 | semidirect |
| 11. C17×#475 | C2 | semidirect |
| 82. Q8×C17 | #41 | semidirect |
| 133. #475 | D17 | semidirect |
| 175. C17 | #3332 | semidirect |
| 217. Q8 | #63256 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763481 | 2 |
| #11763462 | 2 |
| #11763157 | 2 |
| #11763129 | 2 |
| #11763063 | 2 |
| #11763005 | 2 |
| #11762957 | 2 |
| C4×#63230 | 2 |
| #11762886 | 2 |
| #11762809 | 2 |
| C17×#475 | 2 |
| #3332 | 17 |