Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 3. #11763217 | C2 | semidirect |
| 4. #11763216 | C2 | semidirect |
| 5. #11763211 | C2 | semidirect |
| 6. #11763208 | C2 | semidirect |
| 7. #11763208 | C2 | semidirect |
| 11. C17×#499 | C2 | semidirect |
| 64. #63218 | Q8 | semidirect |
| 65. #63218 | Q8 | semidirect |
| 104. #499 | D17 | semidirect |
| 138. C17 | #3166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763365 | 2 |
| #125×D17 | 2 |
| #11763217 | 2 |
| #11763216 | 2 |
| #11763211 | 2 |
| #11763208 | 2 |
| #11762850 | 2 |
| #11762848 | 2 |
| C4×#63218 | 2 |
| C17×#499 | 2 |
| #3166 | 17 |