Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 370 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. #11763343 | C2 | semidirect |
| 2. #11763211 | C2 | semidirect |
| 3. #11763193 | C2 | semidirect |
| 4. #11763164 | C2 | semidirect |
| 5. #11763067 | C2 | semidirect |
| 7. #11763055 | C2 | semidirect |
| 8. #11762922 | C2 | semidirect |
| 9. #11762917 | C2 | semidirect |
| 10. #11762911 | C2 | semidirect |
| 11. C4×M16×C17 | C2 | semidirect |
| 116. C4×M16 | D17 | semidirect |
| 148. C17 | #3183 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763343 | 2 |
| #11763211 | 2 |
| #11763193 | 2 |
| #11763164 | 2 |
| #11763067 | 2 |
| #11763062 | 2 |
| #11763055 | 2 |
| #11762922 | 2 |
| #11762917 | 2 |
| #11762911 | 2 |
| C4×M16×C17 | 2 |
| #3183 | 17 |