Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
406 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 406 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. #11763532 | C2 | semidirect |
| 2. #11763481 | C2 | semidirect |
| 3. #11763198 | C2 | semidirect |
| 4. #11763182 | C2 | semidirect |
| 5. #11763025 | C2 | semidirect |
| 6. #11763015 | C2 | semidirect |
| 7. #11763010 | C2 | semidirect |
| 8. #11763005 | C2 | semidirect |
| 9. #11762911 | C2 | semidirect |
| 10. C4×D136 | C2 | semidirect |
| 11. C17×#446 | C2 | semidirect |
| 106. C8×C17 | #41 | semidirect |
| 135. #446 | D17 | semidirect |
| 173. C17 | #3397 | semidirect |
| 239. C8 | #63256 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763532 | 2 |
| #11763481 | 2 |
| #11763198 | 2 |
| #11763182 | 2 |
| #11763025 | 2 |
| #11763015 | 2 |
| #11763010 | 2 |
| #11763005 | 2 |
| #11762911 | 2 |
| C4×D136 | 2 |
| C17×#446 | 2 |
| #3397 | 17 |