Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
382 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 382 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 |
|---|---|---|
| 2. #11763175 | C2 | semidirect |
| 3. #11763157 | C2 | semidirect |
| 4. #11763106 | C2 | semidirect |
| 5. #11763086 | C2 | semidirect |
| 6. #11763009 | C2 | semidirect |
| 7. #11763009 | C2 | semidirect |
| 8. #11762940 | C2 | semidirect |
| 9. #11762907 | C2 | semidirect |
| 10. C4×#63230 | C2 | semidirect |
| 11. C17×#557 | C2 | semidirect |
| 79. Q8×C17 | #41 | semidirect |
| 120. #557 | D17 | semidirect |
| 165. C17 | #3368 | semidirect |
| 204. Q8 | #63256 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763481 | 2 |
| #11763175 | 2 |
| #11763157 | 2 |
| #11763106 | 2 |
| #11763086 | 2 |
| #11763009 | 2 |
| #11762940 | 2 |
| #11762907 | 2 |
| C4×#63230 | 2 |
| C17×#557 | 2 |
| #3368 | 17 |