Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
340 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 133 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. #11763215 | C2 | semidirect |
| 3. #11763212 | C2 | semidirect |
| 4. #11763116 | C2 | semidirect |
| 5. #11763104 | C2 | semidirect |
| 8. #11762940 | C2 | semidirect |
| 11. Q82×C17 | C2 | semidirect |
| 61. #63230 | Q8 | semidirect |
| 112. Q82 | D17 | semidirect |
| 156. C17 | #3385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763519 | 2 |
| #11763215 | 2 |
| #11763212 | 2 |
| #11763116 | 2 |
| #11763104 | 2 |
| #11763096 | 2 |
| #11763086 | 2 |
| #11762940 | 2 |
| #11762907 | 2 |
| C4×#63230 | 2 |
| Q82×C17 | 2 |
| #3385 | 17 |