Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
390 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 129 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. #11763147 | C2 | semidirect |
| 3. #11763091 | C2 | semidirect |
| 4. #11763086 | C2 | semidirect |
| 5. #11763016 | C2 | semidirect |
| 6. #11763011 | C2 | semidirect |
| 8. C4×#63231 | C2 | semidirect |
| 9. C4×#63230 | C2 | semidirect |
| 10. #11762862 | C2 | semidirect |
| 11. C17×#533 | C2 | semidirect |
| 132. #533 | D17 | semidirect |
| 179. C17 | #3107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#63252 | 2 |
| #11763147 | 2 |
| #11763091 | 2 |
| #11763086 | 2 |
| #11763016 | 2 |
| #11763011 | 2 |
| #11762969 | 2 |
| C4×#63231 | 2 |
| C4×#63230 | 2 |
| #11762862 | 2 |
| C17×#533 | 2 |
| #3107 | 17 |