Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11763529 | C2 | semidirect |
| 2. D4×Dic34 | C2 | semidirect |
| 3. #11763167 | C2 | semidirect |
| 4. #11763160 | C2 | semidirect |
| 5. #11763103 | C2 | semidirect |
| 6. #11763089 | C2 | semidirect |
| 8. #11763014 | C2 | semidirect |
| 9. #11762939 | C2 | semidirect |
| 10. #11762906 | C2 | semidirect |
| 163. C17 | #3367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763529 | 2 |
| D4×Dic34 | 2 |
| #11763167 | 2 |
| #11763160 | 2 |
| #11763103 | 2 |
| #11763089 | 2 |
| #11763022 | 2 |
| #11763014 | 2 |
| #11762939 | 2 |
| #11762906 | 2 |
| C4×D8×C17 | 2 |
| #3367 | 17 |