Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
368 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 368 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. #11763213 | C2 | semidirect |
| 3. #11763187 | C2 | semidirect |
| 4. #11763158 | C2 | semidirect |
| 8. C4×Dic68 | C2 | semidirect |
| 9. C4×#63231 | C2 | semidirect |
| 11. C4×Q16×C17 | C2 | semidirect |
| 87. C4×D17 | Q16 | semidirect |
| 120. C4×Q16 | D17 | semidirect |
| 153. C17 | #3170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763363 | 2 |
| #11763213 | 2 |
| #11763187 | 2 |
| #11763158 | 2 |
| #11763051 | 2 |
| #11763049 | 2 |
| #11763047 | 2 |
| C4×Dic68 | 2 |
| C4×#63231 | 2 |
| C4×C8×D17 | 2 |
| C4×Q16×C17 | 2 |
| #3170 | 17 |