Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 398 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 |
|---|---|---|
| 2. #11763290 | C2 | semidirect |
| 3. #11763152 | C2 | semidirect |
| 4. #11763146 | C2 | semidirect |
| 5. #11763136 | C2 | semidirect |
| 6. #11763124 | C2 | semidirect |
| 7. #11762849 | C2 | semidirect |
| 8. #11762808 | C2 | semidirect |
| 9. #11762806 | C2 | semidirect |
| 10. #11762775 | C2 | semidirect |
| 11. C2×C17×#107 | C2 | semidirect |
| 135. C2×#107 | D17 | semidirect |
| 174. C17 | #3098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763390 | 2 |
| #11763290 | 2 |
| #11763152 | 2 |
| #11763146 | 2 |
| #11763136 | 2 |
| #11763124 | 2 |
| #11762849 | 2 |
| #11762808 | 2 |
| #11762806 | 2 |
| #11762775 | 2 |
| C2×C17×#107 | 2 |
| #3098 | 17 |