Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #11763179 | C2 | semidirect |
| 4. #11763178 | C2 | semidirect |
| 5. #11763177 | C2 | semidirect |
| 6. #11763158 | C2 | semidirect |
| 9. C17×#491 | C2 | semidirect |
| 90. #491 | D17 | semidirect |
| 118. C17 | #3139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763365 | 2 |
| C4⋊Q8×D17 | 2 |
| #11763179 | 2 |
| #11763178 | 2 |
| #11763177 | 2 |
| #11763158 | 2 |
| #11762816 | 2 |
| #11762761 | 2 |
| C17×#491 | 2 |
| #3139 | 17 |