Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
384 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 123 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. #11763187 | C2 | semidirect |
| 4. #11763158 | C2 | semidirect |
| 5. #11763020 | C2 | semidirect |
| 6. #11763019 | C2 | semidirect |
| 7. #11763016 | C2 | semidirect |
| 11. C17×#462 | C2 | semidirect |
| 105. C4×D17 | Q16 | semidirect |
| 139. #462 | D17 | semidirect |
| 178. C17 | #3209 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763363 | 2 |
| C4⋊Q8×D17 | 2 |
| #11763187 | 2 |
| #11763158 | 2 |
| #11763020 | 2 |
| #11763019 | 2 |
| #11763016 | 2 |
| #11762966 | 2 |
| #11762963 | 2 |
| #11762861 | 2 |
| C17×#462 | 2 |
| #3209 | 17 |