Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
376 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 131 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. #11763119 | C2 | semidirect |
| 4. #11763118 | C2 | semidirect |
| 5. #11763105 | C2 | semidirect |
| 6. #11763104 | C2 | semidirect |
| 7. #11763091 | C2 | semidirect |
| 11. C17×#475 | C2 | semidirect |
| 46. Q8×D17 | Q8 | semidirect |
| 134. #475 | D17 | semidirect |
| 173. C17 | #3078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763364 | 2 |
| C4×Q8×D17 | 2 |
| #11763119 | 2 |
| #11763118 | 2 |
| #11763105 | 2 |
| #11763104 | 2 |
| #11763091 | 2 |
| #11762848 | 2 |
| #11762831 | 2 |
| #11762816 | 2 |
| C17×#475 | 2 |
| #3078 | 17 |